In a perfect world, you might have a point in some of these areas. In the real world, as you concede, it would be very difficult to recast all these systems. For example:
1. Pretty much impossible for Colleges to pay "market rate" for a few athletes and still fund T-IX programs on top of the cost to shelter, educate, train and coach all of them. Also, how do you separate each athlete's "value", and determine what part of the team's success is attributable to them and/or where on the developmental curve each athlete is performing at a given time?;
2. If all hospital volunteers were "paid" and residents fully compensated, this would change the hospital economic model;
3. NFP charities use volunteers extensively, from the Red Cross to Hospice care. Are all those volunteers underpaid "employees"?
4. University research laboratories use graduate assistants extensively but keep all the proceeds of their labors and intellectual discoveries. If each was paid for a piece of every patent and discovery, research would probably stop as we know it;
5. There are vastly underpaid "interns" in many segments of the economy. They work summers, or part-time, usually for free or minimum wage. On your model, every single business using interns would have to pay them as full-time employees even though they might not be fully educated or credentialed (see non CPA accountants or non-bar qualified law candidates).
In the college arena, the only (legitimate) funding source I can think of is sponsorships. Shoe companies could pay college athletes, but they'd have to put the money in trust and also get around the Sports Agency Law. That's probably going on now under the table. This would also require some major rule changes to work under the NCAA umbrella.
You are making this way more complicated than it needs to be. Remove the rules that prohibit players from obtaining outside income and they'll get outside income.
I am not saying that everyone is entitled to be paid all the time. I am saying that people should not be prevented from obtaining the value of their work.
If an individual law firm, for example, wants to pay a law graduate less until she passes the bar, fine. If an individual business wants to provide a low-paid internship, fine. But every law firm in America can't agree not to pay non-barred attorneys. (They don't, incidentally. I was paid at the same right as a bared attorney both as a law student intern and directly out of law school before New York got around to credentialing me. Some other firms may have; I wouldn't have gone there.)