Since, you always have to do a Move, in order to roll dice, there often is a "Catch-All" move

Personally, I think it's bad design to have "catch-all" moves in PbtA games. When people have an instinctive "it feels like we should be rolling dice here, which move should we use?" reaction I think it's just fine for the answer to be "actually, we don't roll dice for that in this game". Not everything has to be a mechanized move. Sometimes you'll just say what your character does and it won't map to something you roll dice for as a player, the GM will just say what happens in the world as a result (often you'll trigger the "look at the GM expectantly" prompt for the GM to start using moves from their side). What is or isn't a mechanized move is part of shaping the lens through which a player experiences the situation in a PbtA game. To my mind, "catch-all" style thinking is closer an "I'll just say stuff and let somebody else think about the mechanics" style of play.

The GM having complete choice of what exactly happens on a 6- (instead of taking damage while fighting a Troll, the GM might say: "The Troll takes your puny sword and throws it far away") means that death, unless it actually fits the story well, is out of the question in PbtA.

This may be a question of semantics, but I think that death might "fit the story" any time you're fighting a dangerous opponent. I think there's a "say what honesty demands" element that ought to keep GMs from using their move selection to "save" players who really are in a position to potentially get killed. I remember listening to an AP of Apocalypse World from The JankCast podast where an NPC had a gun to a PC's head (or something similarly threatening), the PC tried some psychic manipulation and got a 6- roll, the GM tried to have the NPC get all flustered and just graze the PC with a gunshot, but the player felt that was really cheesy, that their character dying was the only reasonable resolution to the interaction.

Actively solving problems is not really being rewarded, but a necessity to play the game;

I think there is some rewarding going on in the game, but it can be a bit subtle. If people are playing their characters passively or reactively it probably means they're going to be doing a lot of "looking at the GM expectantly". Which means the GM will be making GM moves, which are probably going to make the character's situation worse. But if the character is proactive they're probably going to be making a lot of player-faced moves, which are often successful at getting them what they're going after. They become the agents of activity in the story, and consequences of their actions will tend to spin off and affect what other characters are doing, keeping the whole situation dynamic and ever-evolving.