I agree, banks should have rules and regulations specific to their industry, just like cafes should industry-specific rules (food handling, tip distribution, etc.).
I don't think "you can't fire a customer" is a good one though.
There's also a distinction between not being able to use a particular bank and not being able to use any bank. It's important that everyone be able to use some bank, but not that everyone can use Chase, but it's tough to regulate that. Again, this is why I see a government option as necessary.