These KYCed cryptocurrencies will lose the "crypto" functionality (no more anonymity) and will essentially become very similar to the other digital government-controlled currencies. For practical reasons they will be just like the bank electronic money that people access through their debit/credit cards or the future CBDCs. However the CBDCs and the bank money will integrate better with the online/offline shops and the government institutions. So the KYCed crypto will not have any advantage over the government CBDC and I expect it to be used mostly for trading on the exchanges by people trying to make some profit from the volatility of the crypto. But no reason to use KYCed crypto in the everyday life if it is does not provide any benefit over the CBDCs.

So institutionalizing a cryptocurrency by enforcing KYC for its usage essentially means turning it into yet another stock symbol that is useless outside of the exchanges.

If cash remains then most likely there will be people who will keep buying/selling real (anonymous) crypto trying it make profit from the volatility of the real crypto. This market will be much smaller by the current one but it will exist.

The major problem is converting between real crypto and CBDCs (and other government-controlled electronic money) at the same time preserving the anonymity of the real crypto wallets and the anonymity of the crypto transactions. I have been thinking about it and it seems that there are various ways to organize this conversion between real crypto and CBDCs as long as the users are allowed to transfer freely CBDCs (or other government-controlled money) from one government-controlled wallet to another without significant cost, i.e. minimal or no government taxes for such transfers. I think that if this problem is solved, then the remaining problems will be solved too.