Bank account diversity. Is it worth it?

I currently have a main current account, a second current account (which I always keep topped up and have things like expenses paid into), and a credit card through a third bank. I pay off the balance of this card every month. I've just been informed that the bank behind the credit card is transferring all of its business to the bank that holds my second account. I've always felt that keeping money in several different places was sensible. I've now realised that I'm not entirely sure why. My instinct is to look for another credit card with a third banking group. But is it worth having this diversity? Part of me is wondering if I'm just being silly. I'm nowhere near the sorts of balances where I'm not protected by a bank failing.