Your TFA requires a phone.
the need to use other time based 2FA without the need of a SMS capable phone to use. Many sites now uses 2FA and a single platform to build it around doesn't make sense.
please use a open system
Vote for the similar suggestion with the most votes: https://twitch.uservoice.com/forums/310228-account-management-e-g-login-connections-pass/suggestions/11498085-google-authentication-for-2-factor-authentication
This. There are plenty of people who don't have a phone or cannot install Authy for some reason or other. Twitch's own advice is to use Authy when "abroad" rather than SMS. If someone cannot install or use Authy, then they have no way to secure their account with 2FA.