Bitcoin is not ready to replace any form of fiat. When it will reach that point, it will just become another form of USD, just maybe without any physical form. Currently it wouldn't be smart to use it, as its too volatile and not regulated, etc.
Bitcoin cannot be regulated at any rate in any point in time, that's the whole premise of a decentralized permissionless system. I don't understand how some people are apparently waiting for whatever regulator to hop in and make the price stable.
Bitcoin price will never be as "stable" as fiat because the supply and other parameters cannot be tweaked in order to achieve this (fictional) stability as they do with fiat.
It can be tho as volatile as gold, and that would be enough. We just need more money sitting on the system so it becomes harder to move. The bigger it becomes, the heavier the object, that is the analogy.
And yes, it's easy to win against Peter's old points. Bitcoin is a better gold, gold is useless in the information era.