Not really, a CBDC would be worse than fiat in the bank, both in terms of control and privacy.
Discussion
1. Both are fiat
2. The government already controls the banks and records are already kept of transactions
Which version is worse isn't the point. It's the primary traits of the thing that matter.
The government can already see your transactions. It can stop your transactions. It can take or freeze your 'money.' It can dictate the terms by which you transact (proved that with the Patriot Act). USD is functionally already a CBDC if you remove cash, which people hardly use anymore.
Of course you could make worse versions. That isn't my point. My point is that people are already basically using one and don't seem as worried as they are when politicians talk about CBDCs. It's already mostly happening and has been for years.