There is nothing to assume about Bitcoin replacing fiat because this just isn't going to happen even in your wildest dreams. What we are speculating about in this thread is Bitcoin getting transacted offline which in itself is an oxymoron by the way. How can you be sure that Bitcoin's price will stabilize itself in the future? It could in 150 years from now when there is nothing more to mine but that's again an assumption. Also, how can you correlate Bitcoin adoption with price stabilization? Have you seen a Bitcoin live price ticker recently? I challenge you to watch one carefully and if you don't see the values changing in 5 minutes or less I will eat my shoe.