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Do whatever you want really; I too have a slew of random accounts that I don't really do anything with.
Ultimately find a financial insitution that works for you; plenty of people dislike Chase checking (basically 0% interest) but I just use them for direct deposit and billpay and then shuffle the rest of the money somewhere else so they work fine for me. I also have random checking and savings accounts at Penfed, Unify, DCU, USAA, First Tech, Lake Michigan, Schwab, and I'm probably forgetting some too frankly.
Like you maybe I should consolidate down some, don't have a use for the Schwab account anymore since got the upgrade to my Chase debit card if I ever need international ATM access again, Unify I've done nothing with, LMCU is another not sure going to do anything with and none of them have a card I'm using currently so not really needed. Oh, NASA and Alliant too, jeez I do have too many accounts if I can't list them off the top of my head haha.

@Anonymous wrote:
I'm just really interested in keeping down the clutter and making it easier for my family if anything ever happened.
Thoughts?
I can relate to this. I wonder if something happened to me, would my family even find all my accounts or would thousands just be "lost"? A simple document listing all your accounts that can go to your family (maybe part of your will) is all it would take. Same idea with insurance policies. How will my family know who to contact? Heck, I am not even sure I know all the coverage I have right now.
I agree with the other folks about putting together a simple clear list of where your money is. Then it matters less whether you have two accounts or ten.
I'd also suggest that you consider whether bank bonus chasing is going to be part of your strategy. It pairs well with the list idea above and you can easily make 1k per year doing it -- far more than you'll likely make in interest.