Nice idea. My only concern is that it could lead to an increase in overzealous removal requests, especially if the idea is copied by other vendors.
I don't. Can you explain?
Over the time scales that archive.org holds on to data, domain ownership itself becomes part of the history. While permitting someone to hide a mistake for security reasons is reasonable, allowing erasure of past owners' history by the current owner is counter to their stated purpose.
Given the prevalence bogus WHOIS data, the inverse is also possible: if the 2nd owner uses the same registrar and "privacy-protection" feature as the original owner, the WHOIS data could appear to have not changed, except for the start date of the registration, which would look identical to a single owner who re-registered their domain after allowing it to lapse.