In Europe at least the banks website won’t function if you don’t auth with their app.
I've read somewhere that some banks will let you use their SMS 2FA as long as you haven't already used their mobile app.
Like, because of a disability, or because you don't have a smartphone? In the latter case, would it work to just go to the bank with a dumb phone?
They also have a different "Talk Device" that is specifically meant for people with disabilities and such, which is supposedly free to get once (80€ for replacements), but the page doesn't specify who can order it.
For example my phone provider has really overpriced international fees ($10 / day) so instead I use an eSIM which usually only comes with data. That means I lose the ability to use text messages or phone calls for any form of verification. A number of banks and other sites also block Google Voice / VoIP numbers.
I used their App previously, and can just switch back to using the website, after authenticating via both sms and e-mail.