Although what Bitsy said about disease transmission is true for a lot of virulent diseases, you have to also consider illness caused by the microbes that all animals routinely carry in their bodies in small numbers.
For example, Salmonella (among other possibly pathogenic organisms) is known to be present in small numbers in most herps, but usually doesn't cause a problem. But if an animal gets stressed for some reason, the numbers of normally innocuous microbes can multiply to huge numbers, leaving the herp unable to cope with them. Then you might get some kind of regurge syndrome going, and the cagemates will only add to the stress. In addition, the cagemates might come down with it too, simply because the microbe is now so prevalent that if conditions are less than ideal, the additional stress could put all at risk. And I believe all of this could happen without any new microbes being introduced to the mix from the outside, because all animals and humans have the makings within us, but in small numbers.
I am not a vet, so this is only my opinion. But it seems logical based on my experience.
Even so, I do see times when an EXPERIENCED keeper might want to experiment, knowing the risks it presents. I think when you proclaim a blanket statement of "don't ever do it", your credibility can be strained for those who do it successfully over a period of time.
I have a herper friend who is a teacher and keeps herps in the classroom. He keeps a lot of native herps in vivs together, much like a community fish tank. They are mostly insect eaters (including green snakes, but mostly lizards and amphibians). I feel there could be a lot to learn from the community tank idea, but it would probably not include corns. I have not yet attempted such a viv myself, but may do so in the future. I think a properly researched and set up community tank could provide stimulation to the animals within, and an enhanced interaction for the viewer. But it also presents new problems and risks, which can also provide new learning experiences for the advanced keeper.
Back when I bred milksnakes, I used to keep a male and 2 or 3 females together for a few months each spring. They ate live fuzzies, so I would feed them and watch them eat (they ate them too fast for one to easily grab another's food item), and keep an eye on them for an hour after eating. I never had a problem, although of course, there COULD have been a problem.
If we have to make blanket statements, I feel it should be:
Beginners: don't cohabitate - you have enough to learn, with enough possible complications, without adding another unnecessary potential problem.
Advanced keepers: Read Jimmy Johnson's post and proceed with extreme caution if you feel you really want to give it a try. Think it over and decide for yourself if you feel the benefits (perhaps a very large cage with a lot more surfaces, hiding areas, microhabitats, and other enhancements not available in a smaller, single occupant cage?) will outweigh the potential risks.