What is the advantage of public key crypto for 2FA, other than that someone who hacks the site's 2FA database can't then impersonate you to that site later, so

What is the advantage of public key crypto for 2FA, other than that someone who hacks the site's 2FA database can't then impersonate you to that site later, so the site doesn't need to do a 2FA token reset on all accounts if there's a compromise? With TOTP, 2FA secrets are unique per site, so a rogue agent at company X doesn't gain very much by leaking your, or everyone's, 2FA secrets. Does TOTP vs public key 2FA have to have a winner? It seems to me like both are fine if properly implemented, and if a public key 2FA system turns into a standard I'm okay with having both. They have trade-offs but for most people and most sites either one is fine. TOTP wins for now because it's a standard and nobody else uses Twitter's system. I don't want an authentication app that only works for one site.