As for alternatives, yes there are, I'm still figuring which ones do not require an app on the smart-phone, though.
I believe I've found a fair alternative after asking a few friends but, I have to account for other factors as well, like, how secure their infrastructure is.
This is because offline 2FA keyfobs were never that popular in Portugal (to my knowledge), unlike 2FA via SMS which I find less secure that keyfobs, but now with the SCA directives from the EU, most banks are jumping on the App 2FA bandwagon. Some do offer a government issued alternative [0] but it still requires an app. I'd be perfectly happy to sign in with my Citizen's ID card reader but that is also rarely implemented (bank-wise), specially since the Chave Movel Digital app from the government [0].
Bottom line, most major banks are going in one direction (deploying their own apps onto customer devices), while smaller banks are staying put (with SMS 2FA) but their security was never that great. So I'm still prospecting and yes, there's a bank co-op on my list also.
Oh, and by "security" I'm mostly going by feel here. Like, if the web interface is a bit jankie I don't feel secure. I'm not going to look into obfuscated .js and pretend like I know anything about web security.
They mitigate the obvious security thread with mandatory 2fa (actually mandated by regulation). Some use this as an opportunity to push their apps: no separate 2fa method, but only integrated in their bloated app, that checks for rooted devices and only supports the newest OS.
It’s quite hard to find out in advance, what 2fa methods with which fees each bank actually requires. I remember that some of them had funny ideas, what a customer should be billed for 2fa SMS. I think it was 50 cents per SMS.