Cooldown for draw offers
One of the problems with that is that if in one position they are losing and they offer a draw, but the next move you are in a drawn position, they won't be able to offer a draw again, and if you don't think it's a draw, you might keep playing it, and that might cause time trouble for your opponent. In case you don't know, making a move automatically declines the draw, so you don't have to keep clicking the decline button.
That's a good point. I also think a good addition to your suggestion is possibly making a move cooldown, and instead of time, a certain number of moves has to be played before another draw is offered, though I can see some issues with this. Alternatively, we can follow the OTB chess rules that one side cannot offer another draw until their opponent offers them one.
Agreed, though usually when I chat saying
"I ain't accepting the draw y'know"
they give up
Etiquette is that if you decline a draw, then it is up to you to offer a draw by the time you have changed your mind.
Besides
"11.5
It is forbidden to distract or annoy the opponent in any manner whatsoever. This includes unreasonable claims, unreasonable offers of a draw or the introduction of a source of noise into the playing area."
https://handbook.fide.com/chapter/E012018