There is no access to cash on the ship. As you said, you won't need cash on the ship, of course, but most ports-of-call require it (i.e. excursions, tips, etc.), and some may not have easy access to ATMs.
On our last cruise, there was a mix-up with the car service that took us to Port Canaveral, and we ended up having to use almost all of our cash to pay the driver. Even though we were in a Category 3 suite with concierge service, there was simply no way to get cash on the ship. We were lucky that our first port-of-call was Key West where it was easy to find an ATM.
Bring money!!