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Yes, with CDBC they can track it, how and where you used it which really defeats the purpose of crypto.
Maybe people don't see the irony that with open blockchains
everyone can track you. Which is one of the main reasons bigger companies avoid to use it as payment. They need confidential transactions to prevent front running in the markets for example.
However, I think someday will might be force to used CDBC though, specially if this is going to be mandated by our government. I mean I'm seeing it as the only "currency" we can used if we want to transact to government agencies. And if it is treated as regular fiat then I guess there's nothing wrong with it. Of course, we still be very cautious of it's usage as as I have said, they can simply monitor us with their CDBC's.
It wouldn't be that different from the current banking systems regarding of privacy. I mean it will be more cost efficient, faster and as a standard, it can be easier to implement to everything. And it would make some current third party payment systems irrelevant. Monitoring is only one reason for it. They are already monitoring money transactions and privacy or pseudonymity on those is pretty much gone with physical cash money going next.