iserith
Magic Wordsmith
It seems to be mostly an argument of semantics? I do get what you mean that players don't/shouldn't usually explicitly ask to make Stealth roll (or some other game mechanic), for example (although depends on context a bit).
However, as far as I can see, it is totally legitimate for players to propose that their PC is using their medicine skill to do something, or their stealth proficiency, or whatever. It is then up to the DM to judge whether that particular usage is possible (or not), and if it is possible whether or not there is uncertainty about the outcome and hence the need for a roll.
This is what I mean by players providing the opportunity to use a skill. It is the players who propose what the PCs are doing and what the desired outcome is. The players (explicitly or implicitly) indicate that the reason for success is whatever (which could include skill proficiency or similar). The DM's role is to judge how to resolve this; either it happens as the players suggest (player fiat), it happens (or doesn't happen) some other way (DM fiat), or a roll is required to decide the outcome.
In my view, it's fine to say you're drawing upon your knowledge of medicine to perform some task. But to say "I want to make a Medicine check..." is establishing the outcome of the fictional action you're attempting as uncertain which isn't the player's role. As a player, I don't want to encourage my DM to ask me to roll either. I'd rather just succeed outright wherever possible. Previous editions of the game encouraged players to ask to make skill checks. This one does not, though players can ask if a particular proficiency applies to an ability check called for by the DM.