I think there has been a misunderstanding on how bankid is used in Sweden (and perhaps other nordic countries too). Yes, you can log in to your bank with bankid, but in most cases you can also log in to your bank with a key fob like device or similar. The problem is that the bankid identification has been adopted by many other online services in Sweden and there bankid is the only option.
* All services provided by the government
* Stock/bond exchanges
* Credit card providers (not banks)
* Insurance companies
* Retirement fund companies
* ...

You will be blocked from many important online services unless you have bankid and changing bank will not solve the problem since the other bank also provides the same bankid. We need an open standard for online identification.