It’d probably be some new PKI on top of SSH where your private key would be held in escrow by an identity provider. e.g. Your username is your email address, and your email provider retains your key pair. It’d probably be portrayed as an improved key management solution that allows more frequent key rotations and revocations. Might even start with being required for government projects, resulting in supported implementations by cloud providers that want lucrative government contracts. Then they just wait for a crisis opportunity like a cyberattack to force ISPs to block non-PKI-based SSH traffic in the name of national security.
And the largest and most paranoid companies that host their own mail and authentication services on-perm would probably be allowed to use those. But most everyone else is left doing key escrow with Google and O365 for their work and personal accounts...