PF2 did this too. I'm not really a fan and prefer the 5E BA. A lot of this has to do with level creating this challenge band where you have these "must be this tall to ride" limits. I get that for a game where folks want to feel progression, but I prefer a world that makes consistent sense myself. That's more the GM in me speaking than the player I suppose. Though, even as a player I sort of roll my eyes at adding +1 for every level.
You're right in that adding +1's every level isn't necessary. It's one of those things that was done for 2 reasons. The first is, that's how it had been done since the very beginning, more or less. You go up a level, your attack bonus increases based on a formula.
The second is kind of a failsafe against falling behind. You can see this in action in 5e as well- character A starts with a 14 Strength and has a +4 to hit. Character B starts with a 16 Strength and has +5 to hit.
At level 4, Character A decides to take a feat that sounds cool to him, let's call it, "Iron Chef Cooking Master". It only increases Strength by +1. No change to attack bonus.
Character B decides to use their ASI as the Gaming Gods intended and raises his Strength to 18, now they have +6 to hit.
Eventually this problem can fix itself, but it may take a very long time before both characters have the same attack bonus.
Any system that automatically increases numbers as you level is setting a floor. 5e does this more gradually, as proficiency bonus only increases a few times over the course of your career. 5e thus sets the floor pretty low, which is fine if you don't want to repeat the kobold/goblin/hobgoblin/orc/bugbear/ogre/troll/hill giant/stone giant/fire giant, etc. etc. loop.
However! And this is worth pointing out. 4e was perfectly capable of doing exactly what bounded accuracy does. You could just raise monsters a level. Done. I ran a Feywild adventure where my 11th level PC's had to assault a mountain infested by Fey goblins (apparently, I was ahead of my time).
Did I have to create new monsters? Nope, I just went to the DM tools, selected "goblin" and cranked up it's level to 10. Huzzah, 10th level Goblins.