My good bank has a password. I actually usually can't remember what it is, but that's fine since it's their password and I'll recognise it when they say it. "Oh, that's right! You _are_ the bank"

But they never proactively asked me to set that up, it's just that I went around this "I can't authenticate to you first, so I'll have to phone you" loop and I pointed out it would work better with a password when I called them back and to my surprise they were like "Yes, we can do that, what password should we say?" and set it up immediately.

So, worth asking I guess?