Bawylie
A very OK person
You seem to be conflating "gotcha" DMing with rolling a skill check vs declaring intention. If PC 1 states "I'm going to attempt to climb the wall" vs rolling and athletics check to climb the wall, my response will be the same. If they're alone as I specified in my scenario the PC may be trapped. If they're together I'll tell them that as they start to climb it's significantly easier than expected; it's up to them to let me know if they stop climbing.
For me, rolling and stating what skill you're using is enough to tell me what you are attempting as a PC 90% of the time. That 10% of the time where it's not? I'll ask for clarification. But neither approach has anything to do with adversarial DMing.
I don't see what not having your sword has to do with anything. I would no more tell a player that they didn't have their sword than tell them they die of constipation because they never mentioned using the latrine.
I’m not conflating those things but now that you bring it up, doing it this way does have the added benefit of AVOIDING gotchas.
So there’s another compelling reason, if you’re looking for one.
As for the sword, I’m sure you can work out why it’s relevant that what’s said and done in game is an important part of play. If not, assume I rolled a diplomacy check to convince you. My reasons don’t matter. I 20’d my diplomacy check.