This is impossible is you consider the financial sector - any kind of unsecured private lending like mortgages become dead in the water, fraud detection goes out the window, money laundering, etc.
If you earned $100,000 in a year but paid $5,000 in mortgage interest, government will not collect taxes on that $5,000, because you gave it to the bank. The bank gets money, but government doesn't: makes little difference if you gave it to the government first (who then handed it on to a bank), or you gave it directly to the bank.
We also know that mortgage lenders use irrelevant---well, scratch that---protected data to make decisions (i.e. discriminatory). Race for example is not supposed to be used in lending decisions.
Fraud detection can probably be solved by other reasonable means. And in any case, if you take the fraud argument to the limit, then you'd end up advocating for constant surveillance to prevent fraud. Equifax, Experian, and Transunion are all horrible companies who do their ostensible job minimally well, while maximizing the exploitation of the data of the people.
It would seem that no one gets to monetize your data but you (to avoid overly invasive questions, the govt could, e.g., regulate the kinds of ZKP questions that the mortgage lender is allowed to ask).
In practice, I'm sure this has some problem, because societies can't function without trust. But in theory, you could imagine something that is more private and harder for other entities to monetize.