the government has them anyway, it's just that in addition to having them, the tax payer also has to pay clearview AI or whoever else for providing that service privately. That's actually exactly how the US government acquires license plate and vehicle data in states where collecting that information directly is prohibited, they just use your money to buy that from the private surveillance industry. [1]
By believing in some sort of mythical distinction between private and public business you've created the worst world of all, in which a government can superficially claim its hands are clean, buy unlimited surveillance data from unregulated private firms, without any democratic accountability. You now have the privilege of filling up Peter Thiel's bank account, while Palantir runs a precrime division that your city council has never even heard of[2]
[1]https://www.theverge.com/2021/1/22/22244848/us-intelligence-...
[2]https://www.theverge.com/2018/2/27/17054740/palantir-predict...