It seems like most internships are not so much a "free trial" for the internee, but an extended, interactive interview and test of skills, personality, and attitude. They exist so that firms don't get stuck with inept workers.

There are also significant costs associated with interns (e.g. training, relocation) which are depreciated if the intern gets hired. Having an intern program like he describes would definitely see an increase in those costs, which makes it a disincentive for firms to have such a program.

That said, I'd love to have the opportunity to intern anywhere at any stage in my life.