AbdulAlhazred
Legend
There are a lot of ways to handle this kind of thing, which is going to vary by table and by system. In Dungeon World (I assume most PbtAs) the player describes their character's fictional actions. The GM then states which move is being made (if any). USUALLY its self-evident and pulling some nonsense is just plain wrong. OTOH the GM DOES have some choices, within the limits of principle and agenda. For one thing a GM is often free to just say "Yeah, XYZ happens" without requiring any move at all, though this is far from always good play. Otherwise the GM will normally do what the player asked for, or in some cases it may be ambiguous and they might pick a move, though the choices are generally pretty limited.When you say ‘the GM is free to say use a different ability’, that sounds alot like what tends to get called GM fiat.
In terms of Traveller, it is still a classic type of game. Maybe you will interpret Streetwise to mean the player gets to choose, maybe not. Even if they choose, they don't have some sort of limitless power any more than GMs ever do. I mean, nobody is realistically suggesting PCs can just dice Streetwise for CR 1 Trillion (enough to build a pretty good Imperial Navy task force in Trillion Credit Squadron). Right? So, there's always a plausible limit. It could be that if the PC says "I want a handgun" and its a Law Level F planet they are not going to get what they want, period. On a law level 0 planet OTOH you might be able to just walk down the street and pick up a PGMP-13 without breaking a sweat or even rolling Streetwise.