My experience with this is that I tend to mess up eventually if I add enough accounts. Each one has its own rules about minimum balance you have to maintain and other fees (especially inactivity fees which have nailed me before). I've also had accounts with banks that required notice in writing to get them closed. So it's kind of like creating a mess; it's more work for you to deal with, you're more likely to lose something if you're not paying attention, and it will take a bunch of work to clean up later.
Nowadays I only open new accounts if there's a definite reward to doing so, like a sign-up bonus, high interest, or some kind of cash back reward.
