Is the balance of your bank account recorded publicly? So it seem there is no need for a public record.
And GDPR does not prohibit voluntary owner entries into a central whois directory, it just prohibits transferring personal data without consent.
Privacy and property rights are interconnected: after all, what is privacy but the right to do with yourself and your property as you see fit without outside observation/interference?
These rights are sometimes at odds with each other: can you really own property if your ownership is not publicly recorded/recognized?