Can you support this with numbers? I think 5e is actually a bit too bounded in some places. I would no worry if proficiency bonus would increase slightly faster.
I'm away from books at the moment. I can be more specific later on.
As I understood it, "bounded accuracy" was (as mentioned in the OP) intended to flatten out the math, have a smaller window of numbers at each tier of play, and etc.
However, there's a rather large difference in proficiency when comparing a character without proficiency in a skill against a character with expertise in a skill. Certainly, someone with expertise should be better, but there are some areas of the game (i.e. Stealth, Athletics to shove, and etc) where that difference is especially highlighted and does not seem to fit the parameters of stated design goals.
Side Note: I've found that using proficiency dice instead of flat bonuses helps.
Similarly, it's somewhat easy to create a character who -even at level 1- is extremely hard for creatures to hit. Over time, new options make doing that even easier as more species have inherent AC bonus and floating ability scores.
High Dex + Shield + Species AC Bonus
That appears to go against the goal of keeping creatures relevant across a wider range of levels.
I'm not sure what exactly WoTC means by "bounded accuracy" but I think 4th Edition (for all the complaints I had about it) made a better attempt at it.