That's... actually a really interesting idea, but you have to consider who you're building the system for - governments, or normal everyday people?
There is a principle, that I think has basically been proven at this point, if not academically:
A: In any non-optional system used by n people, the bad actors using that system are B: It is impossible to prevent bad actors from misusing any system.
C: Trying too hard means the system necessarily damages good actors.
Therefore:
D: Any system that punishes bad participants more than it helps non-bad participants is degenerate.
Bitcoin can be seen as a rejection of a system suffering from C. For perfectly legitimate businesses and people, sending money is an unmitigated pain in the ass, substantial bites taken by middlemen, arbitrary negative action (c.f. civil forfeiture, paypal freezes) and so on. Bitcoin solves almost all of those problems, but makes lives easier for the bad actors too (but not enough that it substantially increases corruption in the world - bad actors gonna bad act)
Now, if your hypothetical system is strictly opt-in, perhaps with social pressure for politicians and such to use it, then I'd have no trouble with it. Were it to become the de facto currency, on the other hand, the problems we have with government overreach and data mining just become a lot worse.
If we accept B as true, then it makes more sense to design for the case of innocent, law abiding people first, out of fear of harming them due to C.
Put another way, I'm a lot more worried about government misusing things under color of law, than I am worried about government corruption. At least regular people can oppose the second one in good faith, while the first one always comes with the "it's legal, so?" baggage.