The very first thing I would do to greatly improve the game and (mostly) everyone's experience with it immediately conflicts with the whole initial premise of taking the game as it actually is and working with that. Which is to lower the level cap from 20th level to 12th level.
I ran 3E and then PF1 for many years. This was my go to move for campaigns. I would either use E6, or I would end the campaign and start anew at level 12-14. My players and I just found the time it took to get to those levels, the game just got long in the tooth. Starting over again starts to sound real good.
Speaking of which, I realized literally only yesterday what the purpose of the Multiclass XP penalty and Favored Classes was. What it does is to discourage players from dipping one or two levels in a class to collect their front loaded main abilities. Like 2 feats for 2 fighter levels, or 8+Int skill points for 1 rogue level, which you can all put into a single skill if you do it at a later point.
Elves are free to dip wizard, dwarves are free to dip fighter, and halflings are free to dip rogue. Which all seems appropriate to give each race as a whole more character and evoke their niche.
But I have to say, in the good 7 or 8 years that I had been casually hanging around Char Op subforums, I am pretty sure I have never seen anyone even mention that Multiclass XP penalties could be a factor. This was something that was in the rule, everyone saw once and thought it was stupid (because they didn't understood what it was supposed to do?), and immediately became common consensus to completely ignore for the entirety of the game's run.
Here you lose me though. Outside a few supplements and 3PP, multiclassing was never a problem for me. Often, you traded power for versatility. I actually found this to be a strength of 3E as part of its infinitely customizable approach to character building.
Actually, I think using milestone leveling is a vast improvement to 3E/PF1 play. Multiclass, crafting, etc.. penalties are a PITA to track and dont help at all with perceived power issues in my experience.
(and remind the players of it in advance, because everyone think it's ignored by default) to put a bit of breaks on the whole Char Ops train that easily runs away from you. In theory, spending time between games on theoretical optimization of your character shouldn't have any negative impact of what actually happens when you play. But in my experience it often does. It's a big part of what I usually call "Searching for the solution to obstacles on your character sheet". And that's what RPGs really should not be about. In combat situations maybe, but overall playing an RPG should not be approached as a math puzzle. You have both a player for every party member and a GM for all the NPCs present who can play all the characters as people. Through complex interactions. It's not a 1980s computer game or choose your own adventure book with dice. I think that for a really enjoyable roleplaying game, players should think of their character sheet as little as possible and imagine the game world as a real place instead. Letting the Char Ops train run away with you is something that I encountered and experienced as one of the big obstacles towards that goal.
I think you hit on a nuanced issue here with 3E play that isnt exactly tied to multiclassing itself. I do think milestone takes some of the burden off character "building" and a bit of the edge off for rewarding "gaming" the system in play. On top of that, multiclassing, as I mentioned, gives versatility to players giving them more tools in the box. Which is huge because 3E is essentially designed to make characters extreme specialists in a given area. Usually, just a few areas at that. So, a typical character has a hammer and a Philips screwdriver, so naturally every problem looks like a nail or screw.
What I am wondering now is, what kind of adventures, campaigns, and play style is D&D 3rd edition actually best at?
I think the adventure path is the answer. During the PF1 era I ran everything from dungeon crawlers to urban adventures. Political intrigue to gothic horror. Linear and non-linear alike. I think the key, however, is you need a specific idea in which the players can specialize around. If you just sandbox an entire setting, sooner or later, a PC is going to be useless. Which is why players guides for adventure paths were so fantastic. They helped players lean into 3E's best bits which is specialization.