My main bank does this all the time.
To be honest, while I'm aware it's not the best of practices, I don't care much. To me, the most important thing about bank security is that if there are fraudulent operations in my account, I can call and have them undone without much fuss. In this respect, my bank has behaved well in the past when random charges from an exotic country appeared in my credit card, in fact they noticed before I did, gave me a call and everything was fixed immediately.
For this reason, I think I'm OK with banks not having too strict security practices. If at some point they start being really paranoid about security, they might feel tempted to conclude that if there is fraudulent activity, it must surely be the client's fault, because their systems are unbreachable. I'd rather have the current situation in which I don't have much responsibility about security, problems happen but the bank responds.