At worst it's no worse than SMS, but at best it's at least secure in transport and effectively free.
The downside to email is primarily that data is not a roaming perk for many. But if it's too access an app then a reasonable assumption of internet access even if not on the mobile is valid.
Also, email delivery sometimes takes a very long time, it can be minutes, if you rely on email forwarding to protect your main email address.
Auth apps are better for 2FA, at least for me.
Separate from that, it is not productive for you to tell me to think about it more -- for all you know I've implemented two factor authentication in various forms for decades (from OPIE when I worked at NRL to Smartcards within DOD to Passkeys currently). What would be more productive is to get more insight into what you're thinking
Does that happen with SMS? Hmm...
To answer your question on whether or not people access other people's SMS accounts -- yes! That's one reason it's not recommended any longer. Additionally, there's often less security possible for ones SMS account versus ones email account.
You would have to get access to their email and SMS to perform a password reset and get past 2FA. If you are saying you could do a SIM swap attack simply by having access to their email I think that is not that practical at all.
> To answer your question on whether or not people access other people's SMS accounts -- yes!
What? I never asked that? What are you even talking about?
Are you imagining that email is used in some other additional way in the authentication process, such as account recovery ?