I recall that the problem was broader than 2FA. They also re-verify accounts that have been idle, or that are being accessed from a new location. Or issues if you've forgotten the password and don't have a phone.
This is exactly it. And if you don't have a verification method on file, Google will just lock the account if it thinks something about your browser or IP address is unusual. Even if you know your password.
Speaking as a long-time Gmail user who doesn't have a mobile, this is kind of terrifying. Sounds like I need to look into moving to Fastmail or somesuch pronto.