I asked a similar question in r/churning and got multiple responses from people who closed their checking and Chase didn't care. There's a rule of thumb that says if you want to keep your chase credit cards don't have chase bank accounts. The reason for this is multiple DPs that if/when they chose to close your bank account, they will close your cards too.

So IMHO, I'd you decide to keep the Chase bank account, keep it very clean and dry. No phumny business of any sort. Myself, I closed my savings and will close my checking next