Here's the big one: why does HP no longer increase?
First off, HP does kind of increase. You do get better at taking hits, but that's through moves that mitigate damage, not through more HP. So while you don't change the number of HP, your ability to take damage can increase, with the right moves.
In the old system we were kind of unequal: player HP scaled automatically, but player damage didn't. That meant that monster HP didn't scale much, but monster damage did. It created this odd setup where a monster would often be dealing far more damage than the players but have as much or less HP.
That's perfectly mathematically valid, but it made the world feel very inconsistent. X HP didn't really mean anything, even abstractly, since X HP for a player meant something far different than X HP for a monster.
Then there's the matter of GM damage. The GM had to be constantly aware of the players' level to be able to use damage well. It was a lot of work! As a GM I tend to think in terms of "that was a minor attack," with HP scaled by level "minor attack" meant something entirely different at low level (5 damage) and high level (15 damage?).
This gets even worse when you try to assign damage to something based on the fiction. Take a rock slide, for example. To me that's something that players shouldn't become effectively immune to through HP accumulation, but in the old system any value you assigned to it would break at some point. This meant that you still had to think of levels. (In fact, despite everything we tried to say, monsters still kind of had levels: you had to assign them a general HP/damage neighborhood that effectively amounted to "what level heroes should it trouble?")
On top of that armor didn't scale well. We had to fit in all these ways to increase armor just to keep it relevant when your HP has more than doubled.
Honestly, the more I ponder it, the more I can't see why D&D has kept it for so long. There's been a general feeling for years now that high level play is pretty much every edition breaks down in some way, in part because "high level" has always meant so many numbers increase automatically. In 3E it was damage, in 4E it's skills. Think of that 4E chart of "DC by level" that means that once you hit a certain level, suddenly the average lock you come across is harder to pick. That's a workaround for the fact that players were always getting better at their skills without choosing to, so DCs had to grow too.
By throwing out automatically increasing HP we gain a lot:
The GM can now assign damage super-easily. d4, d6, d8, d10, done. Just pick one and go. They'll always be dangerous, but never one-hit deadly.
Going along with that, damage sources can be entirely determined by the fiction. You don't need a "high level rockslide" to be dangerous to a 7th level character.
Monsters don't need pseudo-levels anymore. Also, monsters stay relevant for the entire game (more or less). If goblins stop being a threat it's because you've got the moves to deal with them, not because you just happen to have enough HP to soak their attacks indefinitely.
Monster damage, player damage, monster HP, and player HP now all fall into consistent ranges. They're not exactly the same, but a skilled fighting monster will now do damage comparable to a fighter (and often have similar HP).
I know it's a shift from D&D, but I feel its made the game far better. We took a lot of care making first level HP, armor, and damage work really well, and I think we did well with it. The problem was we then had to make 9 more levels all work equally well AND make sure the players scaled with their level correctly AND make sure the GM could scale their monsters and damage correctly. It was a big time sink of tweaking all for what? We can make the players more capable and better able to survive without it.