For
@TheSword and others,
The issue with "handwaving" away travel is you basically just destroyed one of the three pillars IME. Sure, the caster can teleport you all, or you can walk, have random encounters, side quests, etc. and depending on how tight the time line is, you might have to make some difficult choices on what you can and can't do during that travel time and still get to where you need to be before the clock runs out. To me the travel, i.e. the "journey"
IS a huge part of the adventure, not just the destination...
Otherwise, I agree on much of your thoughts. The social pillars and even exploration pillars rarely carry the same sense of danger as combat does and that's a very valid point. After my deep dive into Feats, I no longer feel fighters need more social or exploration support because A) that isn't their main function and B) they can improve in those pillars by using feats, backgrounds, skill choices, etc.
To the other points I am a big fan of compromise: buff fighters (who IMO should be the best at combat but really aren't or barely so) or reduce non-martials combat ability (slightly), nerf casters (just a wee bit, don't need to go crazy if you don't want to).
Other thoughts for casters is have to branches for them: general and specialist. The general branch can do a lot of stuff, and often, but none of it is very powerful. The specialist can only do a few things, not as often, but
man, is their sh!t crazy! FWIW this is what my group is now exploring.
For the people who want superhero D&D all around, build the variant classes to support it.