MarkMc

Don't need X16 this has worked for years. Box Construction, Full Overlay. Set the bottom separation equal to depth desired + 3/4" (in this case 2") and do NOT alter the reveal from default

Select the material -copy and rename or just adjust material- check global symbol mapping

Yes you should BUT calling it a custom cabinet door is a bit oversimplified. More like 3 custom doors and some tricky cabinet manipulation. At least the only way I know.
Parts from a recent one with an adjustment close to yours I think, sides may be a little different.

Open everything in the attached plan, every tab, then try on your own. 
 '
valet cab.zip

Open Defaults, shedules, room finish schedule. Uncheck Room. Then you can delete.

Faster to do than to describe. Here's a rough start.

Add retracted doors either as custom symbol for shelf or insert into back. Replace the rollouts with custom symbols. Replace the counter with a custom symbol so you can change the material. If needing to show both open and closed place another cabinet in the same location on a separate layer and toggle between them.
pantry.zip

There are fewer cabinet folks on this forum than once were. There may be more over at Facebook where I don't go.
 
The short answer:
2020 is for you IF you are interested in high turnover/volume, low to mid range cabinet brands, don’t deal with much remodel of the space, consider a box store your competitor, don’t really want to invest much time in learning or setting up.
 
Chief is for you IF you handle upper middle to better brands (many don’t have 2020 catalogs), want to provide complete, better drawings (to get more referrals from allied pros), willing to invest time learning and setting up, want to outshine the competition, deal with the space/construction regularly, ever push the limit.
 
I used 2020 from version 5.1 to 9.1; exclusively for 9 yrs though supplemented it CAD, PDF, Envisioneer, hand drafting and spreadsheet to fix the dismal pricing. Once I got Chief is still used 2020 in a limited fashion to get item lists for a few years occasionally. My opinion is a bit harsh (and I drank CAs kool-aid:) 
I can't speak to the current version of 2020 though I did keep track of it until a few years ago. Back when I dropped it: support was dismal, stability bad, cabinet pricing unreliably inaccurate, responsiveness to user requested improvements was almost non existent. AFAIK all this was the same as little as 5 yrs ago based on friends forced to use it.
 
All of those are far superior with Chief, with the exception of pricing.
 
What CA does NOT have.
 In CA the Mfg do do NOT have any cabinets in them which also means they will not OOB match Mfg nomenclature. You set up in cabinets in your user library and/or make Style Palettes for them.  Setting up nomenclature often needs to be specific to a Mfg and can get complicated if you want to automate it but there are ways.  CA does not do any pricing. For me this has been a non issue. For years I was already exporting item lists from 2020 to spreadsheet template order forms I made. In Chief I use cabinet schedules to copy and "paste special" into a spreadsheet to do the same thing. In each case I was looking up pricing in a PDF price list. The only difference is that with Chief I had to enter it all (copy/paste). For some brands it eventually became possible to use the spreadsheet to copy line items into an online ordering system quickly as long as the nomenclature is set up properly. There is an advantage to this system though. You become more familiar with costs and then are better able to adjust a job to meet a budget. You can also more quickly compare total cost of variations once you figure out a system to do that with a couple of clicks. Things that CA has
  A robust ability to import symbols, textures, create tile, use any countertop material you can find an image for, any appliance you can find a 3D file of.   Adjust textures, create door styles. I have not found anything I could not draw in Chief that can’t be built.   There are ways to check clearances of hood inserts into custom hood enclosures. Check clearnaces to part of a building, make sure you ductwork can actually be vented. Check clearance for drain pipes when changing locations of fixutres.   Far superior drawings and dimensioning abilities. Benefit below. NOTE- the national average closing rate for GCS (Glorified Cabinet Salesman/aka KD) is 33%. I had a closing rate over 80%. This was thanks to cultivating a stable of allied professionals for referrals where the closing rate ranked in the 90s. Supplying better drawings than the other 30 sources for cabinets within ½ hr drive of me had the best ones come back over and over.
 
A personal note: I was laid off by a Wood Mode Cabinet dealer at the end of 09 during a recession. Got a 2020 license to freelance then coupled it with Envisioneer. Then I picked up an upper middle cabinet line. A year later I got CA. At a time when the many local dealers were opting to sell Chinese cabinets or knock downs I became a QCCI dealer. I immediately ended up with a whole house reno job from a designer I'd worked with; 6 rooms of highly detailed cabinets and two closets all done in CA. CA became a major factor in getting my dealership running and going. A decade later I was drafting jobs for a hi-end cabinet company involving 15 to 30 rooms of cabinets; none of which could have been done with 2020.
 
Many thanks to the folks in Coeur d'Alene.
 

You are using a wall elevation. There is a wall where you get dimensions but an invisible wall behind the island.
Change to a backclipped section.

 

OR setup a default set to do cabinet elevations manually (that's what I use instead of auto dims but you need several for different sets conditions so you can just click and drag)
 
Snip 2- could copy one camera in place, move forward, change technique to line drawing no squiggles or such and gray lines. Stack the two in layout.

Done
cab construc.zip

Here it is as a fixture symbol done in X14. Not sure if your version opens this?
Radius end open cab.calibz

With a custom schedule

 

Since you can't see the wall in 3D AND Kbird1 found that the wall you used is made with Opening No Material  what I think is going on is that you used the drop down menu for wall type and just selected a demo wall. That is an OOB wall (not sure why we have it any longer)
In the video Scott shows makeing a new interior weall type.  I don't think you did that or if you did you did not do it the way he shows (in the video shortly after 19 1/2 minutes)
Image shows 3 types of walls OOB demo from drop down, hatch wall, and new interior wall type. The OOB wall does not show in 3D, wall hatching does not show a different color in 3D, new interior wall does both
NOTE- if  you use wall hatching with a glass house view  for a 3D reference none of the types will show a color; so only matters if you want to see the color in the as built model not in the reference display.

Demo Walls.zip

Export image with  Transparent Background checked- save as PNG.
 
Import into layout-image on left is a quick no effort PBR, image on right is Clay with shadows on.
 

No, long time issue- need to make from 2 cabinets, easier in X13 or 14 BTW. The narrower cabinet has to either overlap the first one or use custom shelf symbols that don't resize.
Did this on the fly ( faster than finding an old plan with one in 12) so not exactly up to snuff but you can get the idea..
 
corner cab.zip

You found the Chief Architect forum so I don't know if you can do this in Home Designer (which has it's own forum) But you can also make columns from cabinets which allow a lot of control and alteration and will take molding. Can then turn those into a symbol which can make placement easier (again all in Chief Pro)
Column on left is one single cabinet, column on right is two. For #2 Copied the first one, then copied in place, adjusted the height of one to be the top, and the other to be the bottom. Changed the molding on the bottom, changed the faces on the top (all sides match front as a side panel inset) and changed the material.

Can even make a round one

you never showed the DBX of the cabinet depth. The dimension used there is the BOX DEPTH same as any make would. Your image shows boxes that are 24" deep for the tall
You can show the doors in plan view by setting that in defaults and turning the door layer on

This is what a label would look like if the cabinet depth were 24" including the door

Is this what you are after?
it's bit easier in X13 but similar principle
Curved panel.zip

You could fudge it with shutters

and custom symbol that has the Y origin offset

Here a ladder shelf made from polyline solids converted to a cabinet door symbol. Read up about symbols, stretch planes, zone and origins. Then open the included symbol to start to get an idea. Sides are easy enough. make the front look the way you want each side and back to look. Then go around to each of those and first select match front, then change that to custom. When done go back to the front and finish it off the way it needs to be.
IF you wanted full height legs with reveal as on the picture you would need to make a custom door symbol for the sides. See below
I'm sure Eric's post will be helpful.

Ladder Shelf cabinet.plan

On quick way- psolid same size as tile, transform replicate to get a second one layered in front. Set back one to say 1/2" thick with emissive material, font one to 1/4" thick to match wall material. Convert to symbol, figure out spacing of tiles on wall. place new symbol over one on say the left side of the wall, check position, transoform replicate to place the rest multiple qty by spacing X and Z PDF with bloom on in camera

With that DBX open press F1 and you will see a section that includes this.

Select the hyperlink Plot Line Views and see this...

So the answer is switch your view type first.

Need to specify a new door/drawer for it. You can just rename them in library. Then they will allow different materials.

You can change the material of the renamed symbol in the library, use a style palette, or in rare cases set as default cabinet.

Start with a full glass wall, change to a pony wall, adjust height. Then a niche works.

From X13 help

 

Might make a "molding symbols" , as opposed to "molding profile". Attached image uses both.  Would still need a symbol for the ends and as JC pointed out elsewhere seperate millwork symbols to use as treatments on the windows.
I put appliques on the front here. I would advise against that, will slog the system down. Just use a picture or simple graphic where needed.
This was made from corbels found in the library-about 15 minutes-didn't worry about much accuracy, but you get the idea.

I usually do it in TurboCad first- some blocks won't but not usually important.
In Cheif- select one line, then "ctrl + J"; click layer in the box, once all are selected,"ctrl + E" (open object) , change color to black (not by layer)