I'm not knowledgeable or experienced enough to give an informed opinion about the pros and cons of new divers hiring a private DM. But while reading this thread, I was wondering: If after doing a checkout dive with an op they recommended that I hire a private DM, would I? I think that I probably wouldn't. I'd rather ask if there were sites suitable for my skill and experience level that I could restrict my diving to. And if there weren't, I'd rather just skip all the diving.
If a dive op is suggesting you hire a private DM, what they're probably implying is that dive sites suitable to your skill and experience (presumably very low in this hypothetical scenario) would not be very interesting or don't exist at all. This is your dive holiday--you traveled a long way to get here--and they want you to enjoy it. To travel to someplace known for spectacular diving and then be relegated to sites that most divers find sub-par (if such sites even exist) seems pointless. Of course, if one doesn't have the skill or experience, one probably shouldn't travel there in the first place. I guess that's what you meant by you'd "rather just skip all the diving." I suppose one could choose to take their dive holiday elsewhere--somewhere more suitable for rank beginners. But in your scenario of already having done a checkout dive, you've already traveled there. So you would travel to Cozumel and then not dive any more after the checkout dive? I know you're just saying what you yourself would do, but I can't imagine many people would do that.
I was a bit surprised when some friends of mine who had never been diving beyond their OW certification dives chose Cozumel as their next dive. But they hired a private DM and from what I understand did just fine, had a great time, and dived all the commonly dived sites.