That exists, but it's a PITA typing codes back and forth, and more importantly no place I've tried accepts it as a login method, other than the bank's own websi

That exists, but it's a PITA typing codes back and forth, and more importantly no place I've tried accepts it as a login method, other than the bank's own website (and it locks you out from some options when logging in like that). Some might work with the BankID application installed on PC (which also only works on some operating systems), and other places specifically requires mobile BankID. So yes, you do need to use the BankID app, not just in case you "want" to use BankID, but in order to be able to log into some sites period.