I last tended into Cancun a few years ago. Wasn't that long ago, but it is unusual now. I think some smaller ships still tender there. It's really not set up for the newer and larger cruise ships. The tender dock is on the NW part of the (inverted) L shaped island. They offer shuttles to the center of the tourist area. They do have nice facilities at the dock for the cruise passengers. Cancun does have the tourist bucks. Or did.
I agree that Cozumel is probably the safest place in Mexico. My friends there say that the cartels do not want to be trapped on the island. The current President has a villa there and there is a lot of security. He feels safe enough to ride a bike through the streets. I feel very good about Cozumel, but I personally don't recommend cruise pax leave the island.
I also agree that the crime stories need to be limited to cruise destinations, and I have warned AcaKev myself.