Why does it have to be Blender 2.7?

Hi. It is not only 2.7. The Sims 4 Studio supports 2.7, 2.76-9. Newer versions of Blender do not work on older versions of Windows which many The Sims 4 Studio users still have. Instead of updating 5574464 versions of plugin every time the new TS4 patch or version of Blender comes out, the developers decided to focus on functionality instead of compatibility.

FBX does not store vertex paint, type and cuts, which are crucial to the functionality of cc.

You can make or edit your cc in any version or software by using Blender as a bridge.
Just export the fbx, edit it in a different software, export back in Blender, add vertex paint, type and cut.
Or instead of opening the blend files in 2.8, you can use append function. Do everything in 2.8+, save, close, open 2.7/2.76-79, append meshgroups from that 2.8+ file, add cut numbers and type, save.