okay, then outright NO! 100% no...How so? Perhaps you misunderstand my point, and I yours. That is to say, beating the DC on an ability check results in the DM granting you success in the goal that you defined for your PC while failing to beat the DC on an ability check results in the DM imposing the failure state. Hence, pass/fail. In other words, any nuance comes in the narrated result, not in the beating or not beating the DC.
th problem is
the goal that you defined for your PC
this also needs to be something bothDM andPC AGREE is the out come...
I can't narrate my Religion check as a way to summon an avatar (But I may if the DM goes with it use religion to do a ritual to call said avatar...if it makes sense). No matter how many times I say "I want to use my Knowledge of Religion to remember the prayer to as for guidance" (and that sentence is a valid one) does NOT then if i make the check let my fighter trained in religion CAST guidance "Okay you remember, you say it perfectly, nothing happens" how ever if he fails the DC he doesn't even remember the prayer right.
so is there a question... yes "Does the fighter remember the prayer?" (the DM can choose to say yeah, or no, or make check to see)
if DM says roll DCXX, all that does is give the fighter the words to the prayer, not the spell casting feature for Orisons (wait that might be me thinking of older editions, maybe they are cantrips in this edition) can the fighter's player narrate "I want to remember the words to the prayer so I can cast guidance." sure... and in this case most DMs (I assume) would tell them "You can roll to remember but not to cast it" or something along those lines.
I can even phrase the action for @iserith Player of FIghter: "I wish to remember using my past religious studies the wording of the prayer used by the clergy of Behumut asking for guidance"
so back to cha skills (that are not called out as being different in the PHB) "I wish to intimidate the kolold to make him tell us where the treasure is." "You can roll to try to be intimidating, but you can't dictate his responce to being intimidated"
DMs that think like me: "The orc growls menecing and tries to intimidate you into running"
Player shouldn't need to say but can: "You can try to intimidate me, but you can't control my fight or flight response."