I will say that I find 90% of criticisms of PBTA systems entirely incomprehensible, in a 'I genuinely can't figure out what you are trying to express' sort of way. (How do playbooks 'limit' the type of character you can play? And how are moves any more constraining overall than, e.g., skill checks...???)
However. I must admit that I do have some negative feelings towards the 'mixed success' mechanic.
It's true that RPGs are mostly storytelling generators, and that drama and conflict keep things interesting. But RPGs are also usually collaborative, and more often than not do involve the players trying to achieve some sort of goal.
Under those circumstances, I find it overly demoralising for the most common roll to be 'something else bad happens' - when 'yes, your helpful action makes things better :)' is genuinely difficult and rare. It makes me want to hesitate a lot before making a decision, because what if I only make things worse?
It's especially bad if the thing you're trying to do doesn't even help. It's not a 'mixed success' if you achieve what you wanted, but it doesn't in any way aid the group toward a goal, and also there is a negative consequence that hampers the group. That's just negative!!! And thing like that happen fairly often whenever there's any kind of ambiguity? Like, maybe when you're searching for a clue that isn't there, or investigating someone who has nothing to do with the crime. Yes, the DM should try and move the story forwards regardless, but that can put a lot of work onto the DM to balance these scales!
Because the thing is, some games really are based around just causing chaos and seeing what happens. River Bank, Monty Python, Good Society (though the latter doesn't have dice at all) - in those, this sort of mechanic would be perfect, because each character has their own idiosyncratic goals, and being able to make progress on their own selfish actions while also causing more chaos for other characters to react to would perfectly enable the kind of story being told! In a game like that, it's more fun if other people mess things up a bit!
But in something like, idk, Monster of the Week? If someone messes up a roll, it makes it harder for everyone to achieve the thing we're working towards. That just kinda... feels bad? And can even foster resentment, if someone isn't playing to their stats or is rolling dice on something unimportant. In those sorts of games, the primary goal is in itself such a big source of conflict that not much more needs to be added.
Admittedly, this last part comes more from listening to a podcast rather than experience playing, but... Listening to The Adventure Time's MotW playthrough, I found myself just kinda stressed out whenever people did anything. Rather than encourage big plays, it did the exact opposite. And it made it very rare to feel like actual progress was being made. Instead, it just felt more like problems were being shuffled around: one gets less bad, another gets more bad.
Obviously, a straightforward 'do x, then y, then z: hurray you win!!' sort of game, or story, would not be very fun. But there needs to feel like a certain sort of build up of actions and intentions for the ultimate result to feel earned, right? If the characters just keep messing up and then suddenly the enemy is defeated... it's not really satisfying. It just feels like it happened arbitrarily, or that they eventually lucked out despite their incompetence. I want it to feel like the heroes won because they did the right thing.
Maybe I'm taking too narrow a view of consequences; e.g., heroes allowing themselves to be injured so as to get a good shot on an enemy usually feels satisfying rather than not. But when you're playing a game as well and you need to make sure your character sticks around to help out others...
I don't know - maybe I'm just too risk averse, ahah. It's kinda funny to me that games which natively don't really have 'consent to die' mechanics can feel less stressful than PBTA can make me feel. Is it also because I'm stressed at the idea of being inspired enough? Coming up with creative enough solutions rather than being able to count on my character's chosen abilities coming through?
Maybe I need more experience with it all. But these are my feelings on the mechanic so far...!