It kinda cracks me up when tourists go to a resort area and try to find "non-touristy places". Truly "non-touristy places" don't want you there. That said, however, there are plenty of places you can go on Cozumel where you won't see any "pod people" or folks that are on an AI plan. As a one-time visitor you may not have found them.
One thing I really like about Cozumel vs other places I've gone and still go along the Yucatan coast is that it's a real, diverse, working community and not just a beach "town" built by and for ex-pats and foreign tourists. If you want touristy or places that cater to American tastes, speak English, etc, then you can easily find them. If you want more local flavor or slightly quieter places, you can find that too. If I'm staying in a condo or somewhere I can get some of my own snacks and drinks, it's nice to have stores to walk to or a few minutes drive away and not have to plan and stock up for a week.
I've been to Australia (an excellent 4+ wk trip that I hope to do again), been to Hawaii a few times, traveled to Europe several times, and to lots of places in the Caribbean and Mexico for diving and non-diving trips. For the near future, for a variety of reasons, we just can't really go places where it could take 2 days to get back home and that we're completely out of touch. For us, Cozumel provides the best of what we want right now - easy to get to, affordable, good diving, a chance to get away and still be "connected" to work and family as needed.