It's not more secure if you use SMS as a 2nd factor and then reuse passwords everywhere, which is a thing a lot of people do.
My understanding of it is if you can use anything other than SMS 2FA then use that and remove SMS, but if your choice if between no 2FA or SMS 2FA then go with SMS. Also, use it stictly as 2FA, not as identity.
This is not my area of expertise so if I'm wrong I would genuinely like to understand why.
My feeling after supporting end users on and off since '95 is they won't differ if they have 2FA or not.
https://security.stackexchange.com/questions/49521/does-two-...
It gets worse if you search around for people talking about how they use 2FA codes to protect their accounts when logging into services on public computers.
The perception of the security added by 2FA emboldens people to make all kinds of poor security choices.
.. which isn't to suggest either password reuse or SMS TFA is a good idea.