Again I see your point. But I've used this system for close to a decade now and I'm only using two master passwords so far. How many passwords have you memorised in the last ten years?
Less than a half dozen. One for the password vault, encrypted phone unlock, PC login, work login and one or two others I'm forgetting. The rest are all just random unique passwords per site.
One issue I see with your hash is using it for sites that have piss poor password policies such as your password can't be over X characters long, or it has to contain letter, number, and limited list of symbols, etc. Your hash could possibly not match the requirements. What do you do in this case?