Although 99% of my interaction with my bank is over internet, that last 1% represents the biggest chunk of money that I will ever spend on anything. That last 1% is by far the most important. For me, anyway.
Another point for me is that I always use my web bank sitting in front of my PC, with a bunch of papers in front of me. 800x480 and thumb keyboard doesn't do it for me when I need to type in 20 digit KID numbers. I don't know how it is with you guys.
As to the BankID application (which is actually just one of several java applets I have seen in regard to Norwegian online banking), I suspect it does lift the security somewhat:
"The initiative, called BankID, aims to become a national ID infrastructure supporting services such as authentication and digital signatures for the entire Norwegian population."
"We have found cryptographic weaknesses that may indicate security problems, protocol flaws facilitating man-in-the-middle attacks, and implementation errors facilitating strong insider attacks. We also note that the system suffers from severe privacy problems."