that nobody can buy any other crypto unless he buys the CDBC and other cryptos can be brought only through CDBC, this would make user identification from them pretty easier.
People either already buy from a centralized exchange after completing full KYC, in which case the government knows everything you do, or they buy peer to peer without completing KYC, in which case the government doesn't know what you are doing. That won't necessarily change with a CBDC. Those who use centralized exchanges will still have zero privacy, and those who trade peer to peer can still hide the fact they are buying and selling bitcoin from the government. The government will be able to more closely track the movement of fiat between individuals, but they will still have no mechanism for forcing those individual to report why they are moving fiat between them. You could be doing anything, from buying a car to repaying a friend.
The idea is that everyone has to know each other's identity when sending a cryptocurrency. That means you would have to know my identity if you want to send me Bitcoin. This is complete nonsense.
I think the idea is that the
government knows everybody's identity. You can still give me your wallet address and I can still send you some bitcoin without either of us knowing anything else about the other, but the government want to know who is sending and receiving those transactions, even if the people doing the transacting don't.