How would people react in this crypto market scenario?

I was reading up on the major banks creating their own private shared ledger to be used as a settlement layer. This got me thinking about how they would do this, would they create their own private coin(s) and police each other? Would they adopt an existing coin they could trust (aka BTC) even if they couldn't control what happened outside their settlement network (I'm thinking it would work like a private lighting layer)? The more I thought about it the more clear it was that they will do anything and everything to take full control of BTC.

Heres the question. Let's say the US government created their own coin, set it as the only official currency & eliminated cash & USD. They offer an exchange, send your BTC to that wallet and get back the new official currency. Same with USD but that's irrelevant. Now here's the kicker, they make it very clear that it will be illegal for citizens to use BTC or any of the alternatives. You have to swap it out or essentially be relegated to the dark & grey markets?