If you make $41k, you still pay 10% on your first ~$10k, 12% on the next ~$30k, and 22% only on that last $1k.

So yes, you could be in a situation where you had been at the top of a bracket, and your incremental wages from the raise are taxed at the next bracket's rate. But it doesn't trigger any kind of situation where your entire salary is now charged at the higher rate.

Yes, of course, a 5% raise does not compensate for 5% inflation. But that's just because taxes exist, not because you are entering a higher bracket per se.

IMO, the whole pervasive narrative around tax brackets being something to fear is a fear-uncertainty-and-doubt move by those seeking to vilify the tax system. It's worked surprisingly well to those ends.

To simplify 100k split 50k @20%, 50k @ 40% is less than (105k split 50k @20%, 55k @40%) / 1.05

The fist is worth 50 * 0.8 + 50 * 0.6 = 70k, the second is worth (50 * 0.8 + 55 * 0.6)/ 1.05 = 69.52k.