To be fair, that's probably the most common thing that happens at my tables too. OTOH, I've got no problems with, "Can I do X with a Y check?" Or, even, when it's pretty obvious, "I try to do X. Check Y. Do I succeed?" As in, "I look around the room, Perception 17, what do I see?"
Yeah, I don't have a problem with that. If the player says something like "Well, can I roll for Investigation?" I'll usually respond with "Maybe, what does that 'investigation' look like?" and let them narrate. I don't mind being flexible so long as it's not too farfetched and the player can really sell it.
"Um, well, my character is going to sort through the rubble at the edges of the room, looking for anything out of the ordinary." Sure Bob, normally I'd call that Perception but close enough, roll Investigation.
"Um, well, my character is going to stare at the sheer cliff
so hard that they see all the hidden handholds and cracks that will let them scale the cliff with ease." You can't
observe your way up a sheer cliff, Bob...you still gotta roll Athletics, but I'll let you use your Wisdom mod instead of Strength.
"Um, well, my character is going to
perform an elaborate
dance and follow some
measured steps to follow the enemy's trail." No Bob, you're not dancing and that' not a Perform check. Roll a Wisdom, Survival check to see if you find the enemy's trail.