The More Bank Accounts the Better?

Any reason not to open a couple more bank accounts for all the gifts/rewards/incentives they offer? Right now I have an old bank account from California (checking and savings) and a credit card attached to it which I use frequently, a new bank account for the city I moved to, which doesn't have any branches of my old bank (checking only), and a credit card with a third bank, that I only use a couple of times a year. This more than covers any banking needs I would actually have, but a number of local banks are offering various incentives to open an account, most enticingly, 75 dollars in free groceries if I set one up. If I am financially able to park whatever the minimum amount is in a free checking/savings account for a year, is there any other downside to opening up a couple more accounts for the rewards? I'm specifically wondering if it does any damage to my credit score, as I understand having a number of unused credit cards would. Is there any other reason not to?