The easy solution is the best one. Just don't collect the info. Any problems resulting from that need to be handled differently.

Proven to work and we wouldn't be dependent on untrustworthy identity providers.

I agree. It is possible, but that does not mean it should be done.

The thing is with such a ZK system you are still collecting and compiling all this data, it's just done by some sort of (government?) notary and there is a layer of anonymity between the notary and the verifier (which they can cooperate to undo).

The real political problem is the concentration of personal information in one place. The ZK system just allows that place (notary) to be separate from the verifier.