Earlier quoted context omitted.
TOTP, unlike a password, can't be brute-forced. If the secret is lost, its game over, but if the secret stays protected, you can't guess it because you can only test the codes, not the secret itself. Brute-force for TOTP would only be possible if you could test 2^6 OTPs in the 60-second window, which would be mitigated by rate-limiting. So it really doesn't do any hard to have TOTP enabled as a fallback if you never…
It’s worth noting that TOTP secrets are more vulnerable than passwords on the service-provider side. They have relatively tiny key space (generally 6 digits), so if the provider doesn’t protect against brute-force, it’s quick and easy to slam the whole key space until you win. They also need the secret in a reversible format, since the service provider has to use the secret to calculate valid codes. So the most commo…
Everything is fed into an HMAC after all. It's only the last step where truncation occurs.