Requiring a TOTP to get into the app handling your TOTP might not be the easiest for most. A strong encryption password on Authy prevents this and you can also disable multi-device / enrollment when not needed.
If Authy wants to not be a joke, then they should end their mandatory SMS authentication method, then. I certainly am not going to trust it when there's an SMS requirement to even get in. Because I (not unreasonably) assume if you contact Authy support and can pass their SMS check, they might have some way of "giving you back access to your account" and by "you" I mean criminals posing as you.
As far as I know, and I may be wrong there, but Authy gives you access back to your account. Not to your TOTP codes which are encrypted by your Backup Password.
Once logged in, you need to enter that "second" password in order to get access to the TOTP codes and Authy will notify you of the new device connected.
