I'm guessing BankID in Sweden is very similar to the version in Norway, which is a pretty horrible service.

In order to use BankID, you have to bind it first to one bank account and use that bank's code brick to log in. Or you use BankID on your phone which is tied to your SIM card and some providers will charge you for using it!

It also relies on your phone having service (not just WiFi access), so the amount you're charged for using it can be much higher overseas.

BankID would be just as secure if they used the authentication scheme behind Google Authenticator, and it would allow people to use it without additional costs.