I can't reconcile the first paragraph with the second. The bounded accuracy problem is that it makes skills less meaningful because everyone can roll; it creates points where having a skill is less meaningful than having the attributes. Combined with the lack of distinction with skill along with the difficulty in getting new ones makes it rough for anyone who wants to engage with it past the most cursory level. Like you talk about how you can't increase skills "out of turn" in PF2, but that's way worse in 5E where you can only get new skills by spending a Feat, which are both rare and are competing with a bunch of different (and often build-crucial, especially for Martials) feats and ASIs. This was one of the biggest problems I had back when 5E started and it's one of the things I've seen people mess around with to create more meaningful distinctions between those who have skills and those who don't. If you don't like plans, then 5E's version of skills is terrible because if you don't plan for what you want at the beginning, you're probably not going to have it (or at least have it for quite a while).
I also don't really get having problems creating a fighter with social skills in PF2 given the spread of attribute boosts they hand out. You might not be able to specialize in every charisma skill, but you can probably get one or two. Like, you talk about "Fighter Skills", but I'm not sure what you really need outside of "Athletics" to do just about all the things you need to do as a Fighter. What are you juggling here?
But honestly, when it comes to level-based systems, I generally think PF2 does a pretty good job of it. There's a lot more room to play with and use GM's discretion without breaking the system; it's easier to hand out a skill in something because it doesn't instantly boost up to maximum like 5E, while it's also harder to max out and break the system through numbers given how the actual math works.