Your phone is indeed a SPOF. If you lose your phone, you're fucked in a variety of scenarios. To say nothing of services that require a custom app and accept nothing else.
And I can't even install the app on a second phone, because: ah, ha! Only one at a time! There is no installing two, Luke. Only one there will be. (There you go... quotation inception.)
1. OP is asking smartphone; SMS 2FA does not require a "smartphone", but "mobile phone".
2. Alternative options mentioned above should you be in the misfortune of losing your... "phone"
Sensitive, ha?
> 1. OP is asking smartphone; SMS 2FA does not require a "smartphone", but "mobile phone".
Nitpicking and strawman argument. They're both part of, and compounding, the same problem.
> 2. Alternative options mentioned above should you be in the misfortune of losing your... "phone"
Sure they "should", but they're often not offered... even if you insist.
And more often than not, the alternative options available take weeks of phone calls and visits to the local (if you're lucky to have one) branch office of your /whatever service failed you/.