Exactly. The CBDC will certainly be prevented from being used with centralized exchanges.

But whether it will work as a payment method for P2P exchanges will depend on whether or not payments can be reversed. In Kenya, for example, m-Pesa mobile money payments are not easily reversed (without permission from the recipient, such as when payment was sent to the wrong phone number). So that specific mobile money, ranking high on the "hardness scale", works well for sellers (being not easily reversed) as well as for buyers (easy to acquire, ... as m-Pesa agents take cash deposits and are found everywhere).

The May Scale of Money Hardness and BitCoin https://blog.stakeventures.com/articles/the-may-scale-of-money-hardness-and-bitcoin

Payment methods https://en.bitcoin.it/wiki/Payment_methods

The only thing government can do to stop the CBDC being used for P2P trading is to perform sting operations, ... where law enforcement make trades and then can identify who is selling (and maybe targeting those who are buying as well). That's a very expensive approach, in labor costs and in other resources. But, for example, in Nigeria the government did that and gave lists of traders to their banks with the insinuation that further service to those individuals makes the bank a party to future money laundering charges that may occur from further activity by those individuals.

Another reason a CBDC could help further adoption of bitcoin is because a CBDC gets used as a substitute for cash. With fewer cash transactions occurring, cash becomes harder (and more expensive) to use. Want to withdraw cash from a bank? Use the ATM, and oh ... there's now a fee to do so (or a higher fee, if you are already paying fees to use the ATM). So more merchants may add bitcoin payments for those who prefer to not use either payment card or the CBDC.

And most CBDCs are likely to be for domestic transactions only. So a CBDC doesn't displace bitcoin for cross-border payments.

Overall, I can't imagine that CBDCs will be necessarily good for bitcoin, but them existing doesn't mean bitcoin is significantly affected negatively either.

And I expect CBDCs to be much ado about nothing, especially after seeing the path of Nigeria's eNaira CBDC, a year later now since it launched ... and it is going nowhere. The CEO of BitNob nailed it: "Dead on arrival."