Also, how will sending a new password to your cell phone help? If you are dealing with state sponsored actors, why not assume they can see all text and email?
That said, I find SMS-based 2FA to be pretty dodgy as well. Cloudflare was hacked once by somebody who managed gain access to an admin's mobile phone by social engineering their telco. If a site does not offer TOTP based 2FA I usually don't bother using it.