That's not how that works - they can prove they check by showing logs, rather than VPs. There's even legal limits on what identifiers they can store and for how long. But even ignoring that, they'd be storing only very limited disclosures.
The base registry stores identifiers of issuers and verifiers, not credential holders.
Even the status register does not contain the tokens themselves:
> Within these status lists, each index (i.e., status entry) documents the validity of one VC. The corresponding index is captured in the VC’s metadata to allow for a decentralized status information retrieval that does not require verifiers or the VC holder to contact the issuer.
Of course, each issuer needs to maintain a list of the credentials they have issued in order to be able to ever revoke them. That's unavoidable.
The base registry stores identifiers of issuers and verifiers, not credential holders.
Even the status register does not contain the tokens themselves:
> Within these status lists, each index (i.e., status entry) documents the validity of one VC. The corresponding index is captured in the VC’s metadata to allow for a decentralized status information retrieval that does not require verifiers or the VC holder to contact the issuer.
Of course, each issuer needs to maintain a list of the credentials they have issued in order to be able to ever revoke them. That's unavoidable.