The video's last question's premise, which Reggie explained about P2P without the middleman but the person said is not about P2P transaction; I suspect his actual premise is whether bitcoin will totally displace central banking altogether, because we are still using fiats to get into cryptos.
I would say yes.
And whether my suspicion is right about that person's actual premise will need Reggie to confirm.
It's an interesting question. It just depends on who takes what currency. If I can start paying all of my bills with crypto I don't need fiat.
Governments and central banks are loathe to give up control and easy profits for being middle-men. It may be that at some point laws would prevent certain entities from accepting a non-federal crypto (because I think the federal reserve may eventually establish its own crypto dollar) thus forcing use to convert crypto to fiat to pay certain bills. But if the local grocery store and utility companies take crypto, who needs a bank any more? Think about why you have a bank... #1 so you don't have piles of cash laying around (ie Security/Risk) and #2 so you can cash checks and write checks. Crypto addresses those needs.
Once people un-bank, the fractional reserve lending system goes away and with it the fed's ability to control the money supply.