I propose an experiment: next time a player declares an intent without specifying what their character does to try and achieve it, ask them, “do you want me to decide how your character goes about trying to do that?” I’d be willing to bet they will say no very close to 100% of the time.
But, in doing so, you are implying different stakes for the choice than were initially presented.
If you didn't signal that the choice particularly matters, they won't specify as if it particularly matters.