Such a great question that I’ve also struggled with. You essentially hit a wall trying to preserve privacy whenever banks and real-world payments are involved.
Privacy and the other virtual card vendors are great at isolating the threat of card fraud and creating a layer between your transactions and your bank, but they also operate in the same regulated environment as the banks and all use third-party KYC providers like Plaid, Sumsub and Persona to satisfy their compliance and AML requirements because it’s probably too expensive and cumbersome for them to build their own KYC service.
Unfortunately, each of these KYC providers operate like a black box so you never really know how they’re doing their checks and if they reject you, they’re not even legally allowed to tell you why. I can only suggest that you request your personal data from each service to understand what they currently have collected and look for clues as to what the discrepancies may be.
Unfortunately most of them don’t make this easy and simply ask you to send a free-form email to privacy@blahblahdotcom with your request, rather than making it easy for everyone to do in a self-serve manner (presumably to discourage this behaviour as it’s manual/time consuming for them).