Sure, for now. If it ever reaches wide adoption, when Google/MS/Apple see only 2% of users use a 3rd party to store keys, why would they continue to maintain the ability to integrate? Especially if there's some advantage (lock in) to not doing so.
Multiple devices/key stores that don't sync are dead before they even get started. Almost no users are going to be willing to do that, and thus most websites won't bother to support it. How many websites today offer the ability to have multiple OTP options concurrently and/or allow you to only enable TOTP and disable email/SMS?
This will start out open and flexible to gain adoption, and then either through malice, laziness, or low adoption, the options that avoid lock in will be phased out.
Multiple devices/key stores that don't sync are dead before they even get started. Almost no users are going to be willing to do that, and thus most websites won't bother to support it. How many websites today offer the ability to have multiple OTP options concurrently and/or allow you to only enable TOTP and disable email/SMS?
This will start out open and flexible to gain adoption, and then either through malice, laziness, or low adoption, the options that avoid lock in will be phased out.