True. But it would be quite annoying when faced with a troll who would keep offering you a draw every move!
Yeah, maybe. But it shouldn't be something you need to respond to, just more visible.
I've played in vote chess games where all 12 players missed a draw offer.

I recently missed a draw offer in an online game -- I didn't see it until reading through alerts later. Granted, it was my oversight, but it would be useful for there to be a more robust notice on the game-board screen when a draw offer has been made in online chess. When I am looking through my online games, I am focused on the board and pieces when I pull a game screen up. That's where the notice would be most useful for me.