They will not replace fiat. There are many reasons.

But they will become the backbone of financial structure.

As far as regulation, it's nonsensical for the most part. First it's decentralized all over the world. It is peer regulated. Nearly every possible application of existing laws is for reasons that cryptos are immune to. The point of conversion is from fiat to crypto where regulation needs apply again. The other case is when cryptos are used in exchange for goods and services under the purview of a government - up until that time they are not no matter what lies Coin Center and know-it-all officials claim.

Consider this, once you have cryptos in a peer regulated system being used for liquidity of funds the government no longer needs to spend time and resources on them since they're immutable and essentially 51% attack impossible. That's ONE reason they aren't in the tax & regulation jurisdiction. (although illegally right now people claim they are)