Account recovery is a major pain point for any site that supports TOTP 2FA. If you're not using a TOTP application that supports cloud backup (like Authy), when you lose or replace your mobile device the existing TOTP tokens are useless as they can't be recovered. This results in some type of account recovery process to reintroduce the 2FA tokens. Often these recovery processes introduce additional security issues that are equivalent to not supporting 2FA at all, or they might require costly human intervention.

Don't get me started on SMS 2FA.