Heat travel towards Cold in ALL directions. It doesn't matter the orientation. Hot air rises because it is less dense than cold air.
We insulate attics (and floors) with more insulation because it is easy (costs less). More heat escapes through the walls than the ceilings in most structures. The formula is: Surface area x U-Value. There is an orientation component to the air film layer used in U-value calculations (vertical through horizontal), but there is no component in U-value calculations that concern whether a component is part of a ceiling versus a wall.
2x6 walls are structurally stronger than 2x4 walls. 2x6 studs cost more (more material, weight, volume, etc). If you don't need a 2x6 for structural reasons then DON'T use them. A decade ago the nominal cost between a 2x4 and 2x6 was pretty nominal, so it was a pretty easy solution to utilize a 2x6 wall to meet the energy codes.
The IECC Energy codes look at the thermal performance of the wall assembly. A 2x4 wall with a continuous rigid foam insulation layer (inside or out) has a lower U-value than a 2x6 wall with just cavity insulation. The IECC Building code covers structural requirements. You as the designer (or builder) must design the building to meet both components of the code.
I would suggest anyone reading this start looking at the IECC2021 codes, and play with the corresponding (web-only currently) version of ResCheck to get an idea of what's to come with a much bigger emphasis on building assembly U-values. IECC Codes ResCheck