I like this position, which occurred after my opponent made a critical error. Black to move.
You advocate ruining the importance of such positions.
I mean you are right, and I don't know how to fix such a thing I suppose it's really a question of what you value, do you want intense games with crazy attacks, or do you want a game where 3 hours go by and one guy who has clearly lost the game on a strategic level finally goes "hah! Technically I didn't lose! Wasn't that entertaining! I'm so glad we sat here for 3 hours!"
King versus King bishop.
Literally no way to checkmate or stalemate. Both sides know, neither can win. The game has been one of attacking, yet it came down to this. What do you propose? They play until timeout? What if the side with a king is faster? Then does he win and impossible game? WHAT ABOUT KING VERSUS KING?! Playing until time out means 400 move games as masters have increment and only lose when they drop dead. Draws are the way to end unwindable games, or to give weaker players chances against better ones. By getting rid of draws people won't be more aggressive! They know they either win or loss and play slowly, not fighting their opponent so that their opponent miss steps. Their opponent does the same. Cue a 500 move game of maneuvering. Is that what you want chess to be? Plus your, white has an advantage, That is stupid as white's advantage is negligible and most opening lines negate that anyways. Under your ideas anyone could just trade every chance they get as black and win due to your dumb King versus king principle. White would have to no trade, not give chances to trade, and virtually stay on the first, second, and third rank in order for black not to just trade everything and win.
I feel like your idea is good but your reasoning isn't, not to be rude. You put up a good argument, but draws help chess by teaching them to look at their moves and mistakes. I would keep draws, but your ideas are decent, too.