You already have good info here from others, but if any doubt, I just returned from a trip to Coz with my family. Main purpose was to have my 10 year old granddaughter do the Discover Scuba Diving. She is a fish in a pool and did the "Bubbler" experience at age 8 and 9.
We stayed at Villa Aldora, so did the DSD with Aldora Divers. First day my son (who in 1998 didn't complete his last OW check out dive - he was 11 - with my wife and me) and granddaughter did the pool work (at the Villa) and then moved over to the ocean for a 60 min+ shore dive. I grabbed a tank and met them 10 minutes into their dive. It was about 15' max. Did see a nice drum fish and an eagle ray.
The next afternoon, my granddaughter and I went to a little used dive site - San Clemente (popular for snorkel tours) - and did a 70 minute dive with max depth of 30' and no current. I was the best "buddy" diver I've ever been for anyone I've ever dived with and that includes my wife! when she was diving! Since my camera flooded and I couldn't use it, it was also one of the most relaxing dives I've ever done. Saw a lot of fish and a turtle. Also had a new Rescue Diver and new AOW diver with a handful of dives on the boat with us doing the same site with a different DM. Granddaughter had a great time.
My thought process is that many places get mixed messages for various reasons. I've even thought diving to be suspect on an island until I went a 2nd time and dove a different area which changed my mind. If I were looking at Coz for the first time and knew that it was a popular place that many people like (even though there were mixed messages), I wouldn't have second thoughts about trying it. Dive ops will take you to the marine park and through the course of several days of diving, I would hope to get a taste of what Coz has to offer.
Many good ops in Coz can set you up for the type of diving and depths you want. Where you stay might be a factor on who you dive with. There are options in Coz. One is the convenient way - dive resort with dive op onsite. Some of those will be all-inclusive with large boats (many divers), but some aren't AI's and have small boats (such as where I just stayed - Villa Aldora.) You can also stay at hotels/resorts that have a pier or are within walking distance to a pickup pier. Another option is a taxi to the dive op or to one of the marinas to meet the boat. Attached the link to my spreadsheet that may have some helpful info in choosing a dive op.
Cozumel Dive Ops