Would a payments company benefit from maintaining checking accounts at multiple banks?

For instant funds settlement using their own money, opening an account with each bank will do the trick, fast! That is one advantage a payment company will open an account with each bank. The problem becomes if they have access to APIs to instantly do an intrabank funds transfer.

They can net off at the end of the day or the ACH cycle period and the cost of funds for 3-5 days can be built into the cost of the service.