What is the point if bitcoin price become stable? Bitcoin a trading/investment asset, if the price is being stable for too long time then I'm afraid people will start to leave it because stable price = less profit in term of trading.
Bitcoin price will never stable imho and it wont replace fiat money forever. I do not even hope it will replace fiat money, I guess many others also hope the same with me. I will only agree if bitcoin is just an alternative payment of fiat money.