I agree it's not desirable to share a computer. How bad it is depends on the dives, the people, the computer. It's certainly less dangerous than some of the stupid tricks I've heard, like the people who bring spare computers and start using a new one when they bend the first one, or go into deco because they have no clue what their computer is telling them. If you have the buoyancy control and awareness to really stick with your buddy and keep the computer same depth or deeper all the time, and you're using a conservative computer like the Gekko, and aren't near pushing NDLs - it's pretty low risk even though few will recommend it. Opposite scenario where you're diving more aggressively and don't have your act together, you're more likely to get into trouble.
I will point out something that I don't think has been said so far. A computer should make your typical tropical diving more convenient and give you more flexibility, and you lose some of that when sharing. It may also get you more bottom time, and you could lose some of that when playing this game too. Keeping the same depth or the computer always deeper is one thing - and it's going to be less relaxing as a new diver if you're constantly thinking about this rather than watching the fish, and annoying when one of you wants to duck down for a bit and peek under that interesting ledge. But what if you don't even do all your dives together? I dive with my husband most of the time. But during a trip there will almost always be times where one of us doesn't go and the other person dives with someone else. (Stuffed up, ear problems, tired, too lazy to do a night dive, whatever.) Or times where we both dive with someone else for at least part of a dive - sometimes you get to know the folks on your boat and buddy swapping is convenient due to differing air consumption.
You also lose the redundancy of the second computer, and the sanity check a second computer can provide, and the redundancy of having 2 people keeping an eye on their computers (or are you so glued together you're both watching the one? That will be a pretty annoying way to dive.)
My take is, if you can spring for a trip to Belize, spring for another $300 to buy a second computer or rent one, for practical reasons if nothing else. I would only get a Nitrox computer if buying new, but you can probably pick up a used air computer for peanuts.