Bitcoin isn't internet. Internet is something that has no alternative. We can currently pay in fiat and I am quite sure that we will be able to do that in 2100. I don't think Bitcoin will ever replace fiat. Governments simply has so much power.

Bitcoin is non-inflatory. That allows it to be used as a storage of value. It will be safe heaven for investors and it's volatility will be used to gain wealth. These reasons could tempt new investors in and that way increase Bitcoins market cap. If we see inflation as a way to move money from poor peoples pocket to rich peoples then the rich are fine with fiat and the rest of the world are fine with it as well.

Neither of these scenarios will lead to higher adoption but higher value only.