Instead of going through the motions of a roll that is doomed to fail even on a 20, you could just cut to the chase by simply narrating: "as the party member with the best chance of breaking down a door, you give it your top effort but this door seems to be immune to your physical blows. What do you want to do now?" If you make them roll, and they roll very low, it could trigger the dreaded "waterfall" of rolls among the entire party where each player is hoping for a very high roll to succeed. IMO, better to narrate (or, perhaps like you said, tell the player that the DC is beyond reach for that strategy) and let the players move on to some other solutions.I agree - one I recall was a magically warded door with an exceptionally high break DC - so high a PC rolled a natural 20 on an Athletics check and still failed to open it. If I had said "Don't roll" then they wouldn't have attempted to open the door or wouldn't have received the information that the door was incredibly hard to break.
Often though I like to tell players the target DC so they they can tell me "I auto pass" or "I can't make that".
In any case, different approaches suit different situations, different GM styles, and even different genres. And the 5e guidance is very supportive of a variety of approaches - it seeks to empower the DM, not constrain him or her.