To where, the site requesting the verification? Now it is no longer zero knowledge.
The government shouldn't know if/how many times I use my ID—you would be essentially building a country-wide blackmail database since it's a near direct proxy for porn usage. And it doesn't even matter if it's true, people will assume it anyway.
Your system effectively collects exactly the data ZKP is intended to protect.
Which is a long way of saying "ZKP" isn't an answer to this problem because you can't actually have zero knowledge in a system where people have little incentive to keep their key a secret.
No third part would know how often you use your ID.
Why do people make up problems that are already solved?
OTP and biometrics aren’t new security features and people don’t assume the government gets informed every time they use it.
But also, this on-device fingerprint MFA would presumably be fairly bypassable. E.g. just glitch the device to extract the private key. ... and of course all the power hungry / extra complex ZKP machinery means less resources spent on preventing glitch attacks.
"Just use existing OTP" is a model that assumes that people actually want to protect their credentials. This is a Netflix password sharing situation and OTP didn't solve it.