First off, I agree with almost everything you have posted, and have respect for your opinions. But I disagree with the bolded part above.
If the NCAA allows players to sell merchandise, or tickets or anything that was given to them by the institution, it would not be long before the players got more and more merchandise, and there were more and more "fans" who show up with a great interest in having the "collectible item", and paying way above market price for it.
How many tOSU boosters would be showing up with wads on $100 bills and saying "Wow...a game worn jersey? Sure I'll give you $2,000 for that". And that would really tilt the balance to the schools with the most money.