(Well I could be happier if they supports TOTP, but I'm not holding my breath)
TOTP or stronger, please.
TOTP just "feels" more secure.
TOTP is more secure because it isn't tied to a phone number. You're right that it's still phishable but that's not the point.
In both cases, the primary benefit to the general population is to have a rotating credential that, if one website is hacked, is useless on another website.
You fully control how to store the TOTP seed and how you compute the value, so it is far more secure.
Yes, it can be phished if you fall for that, but it removes several attack vectors.
Sorta. The seed still needs to be issued to you in some way.
How was the first factor (the password) compromised?
Assuming the user is using site-unique passwords, in 99% of cases where an attacker obtains a functional password they can get at least one TOTP code or the seed in the same manner. (ie, if I can steal your password DB, odds are pretty good for me stealing your TOTP seed DB as well.)
The outcome of a single successful authentication is a longer-lived session cookie. Once an attacker has that they can reset your creds (usually just requiring re-entering the password) and the account is theirs.
IMO, the only 2nd factor that matters are those that mutually authenticate like PassKeys / FIDO keys.
One of the biggest weaknesses with TOTP apps I've tried using is that you have to remember to transfer them to a new phone before you get rid of your old phone. I once got locked out of a domain registrar because I set up TOTP on an old phone many years back. That was long gone by the time I wanted to do something with my domain.
TOTP is fine, but always give me recovery codes I can print and out and keep with my other important documents. Too many services don't do that.
TOTP -> Time-based One Time Password SMS -> Delivery mechanism.
You can deliver TOTP over SMS.
Obviously, SMS shouldn't be used, but I was under the impression that the code generation mechanism and the code generation algorithms are completely disparate concepts.