Well, first off, snakes already have a well developed and highly effective auto-immune system, as well as a high risistance to sickness. They are amazingly adapted at thwarting off ailments such as respiratory infections, infectious stomatitis(mouth rot), and certain diseases, and additionally to heal tissue wounds without infection taking over. It's when they get stressed for any number of reasons that things can go "down-hill" fast. Also many wild snakes(and captive ones) are likely to harbor a certain amount of internal parasites as well, this is quite normal for them to be a "host" to some parasites to a certain extent.
Most rodents also harbor Pinworms and other parasites to some degree, and any other number of possible flukes, Cestodes, Trematodes, and the like. Snakes systems are well adapted at coping with these levels of parasites to a great degree.
It is known that if stress and parasite levels become too high though, that serious problems can and do arise.
So without adding more parasite loads to captive snakes with offering live, they are less likely to have problems. This is certainly NOT to say that feeding live rodents will cause problems, because it is not necessarily the case, but if given the choice, and weighing the pros and cons of both, most prefer to feed F/T rodents. Just to also add that I've fed tons of live rodents to snakes over the many years too, but there really isn't a reason it must be live prey, and several reasons people go with frozen, not to mention the handiness.
Also, if a snake gets a bad constriction hold of a frantic rodent, the rodent will bite whatever is within biting distance of it's mouth, eyes, mouth body scales, etc... that can cause big problems. I've seen this many many times myself, and who wants an rare expensive snake, or ANY snake for that matter in their collection getting bitten?.
In any case, I'm not so sure I answered your question directly, but this is my opinion regarding this.
~Doug
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"Better to be silent and thought a fool, than to open mouth and remove any doubt!"