I actually do let mine sit out in the air for a few days. But I live in a dry climate. It also all depends on what MP base you are using. Some will sweat like crazy if left out and get any humidity on them. Some get really dry. But some do just fine.
I've found some of my old MP soaps, like 3 or 4 years old, and they were left unwrapped and definitely lasted longer when we used them since the excess moisture had dried out of them.
Also, the vegetable glycerin used in MP bases is not a byproduct of CP soap. It is created by hydrolysis (extraction) of the vegetable oils' crude glycerol fats. Basically, the oil is heated to a high temperature of above 400 degrees, under pressure with water. The glycerin splits off from the fatty acids, and is absorbed by the water. Then it is distilled to remove the glycerin.