Herlock Sholmes: there are two guys who want to play chess for some stake, and agree that they can raise the stake during the game and if the opponent refuses to accept, game ends and the money belongs to the one who offered the doubling ... could you tell me what is wrong with this scenario

For one, this has no analogy with BK. In BK, you win, draw or lose. There are no other outcomes. There's no "winning by a larger amount". If you play a 10 point match, you get the same reward regardless whether you win 10-9 or 10-0.

Second, that would mean the stronger player would offer to double the stakes at the first move, while the position is still equal, instead of waiting till he has an advantage, in order to maximize his chance of playing for doubled stakes.

Off the top of my head, I'd say the draw problem could perhaps be solved by counting draws as 0 points instead of 0.5. Wouldn't that cancel all speculations about doubling in a drawn position?

Draws are a fundamental part of the game of chess, and very common. Scoring a draw as a loss is a big change of the game. You might as well replace the rooks with diamond aces. It just doesn't make sense.