Would it be valuable to have a bank that other banks wouldn't/couldn't deal with? What are you trying to accomplish?
Basically what I want is a way for people to purchase bitcoins, and "store" that value with a "bank" somewhere. I don't care if it's in tim-buck-too. And I don't care about being able to transfer money to and from other banking institutions.
Online Poker Websites for example... they couldn't get jurisdiction in Las Vegas for their "Casinos"... so they went to native reserves in Canada (possibly an option for us, natives will change any of their laws in exchange for money)... and tiny islands in the middle of nowhere, and setup their "Casinos".
Does anybody regularly check on their methods and processes? Probably not.
Does anybody reprimand them if money is lost, stolen or misappropriated. No.
They run a fairly lucrative business, and that notion alone is enough for millions of people to log on and desposit their money every week.
I bet if you asked all of the pokerstars.com players "Where is pokerstars located?" they probably couldn't tell you, and they probably don't care.
Thanks for all of the great discussion/insight guys. Let's keep it going.