It has nothing to do with the purity argument. The NCAA is more than just football and basketball - it covers 24 different sports across three divisions. Killing off the cash cows of football and basketball by eliminating them for the NCAA (which is where we are headed, IMHO) will effectively kill off the 22 other heavily subsidized sports.
What tends to be conveniently and constantly ignored is the fact that the NCAA is a member-run organization, whose members collectively agreed on the rules of the organization. It blows my mind to see people viewing the NCAA as this third party entity intent on world domination motivated solely by greed. It is the collective 1,098 member schools of the NCAA that steer that ship. If you can imagine, the real direction is likely provided by a select few institutions that hold extraordinary power within the organization. But if you think trying to get 535 individuals to cooperate in effectively and efficiently running this country is difficult, imagine almost twice that many trying to run a much smaller entity . . .
If the athletes want to be paid, and knowing they are not likely to make the bigs, then pay them. But pay them wages what can be supported by whatever organization is going to emerge from the mess, which is likely to be a piss poor quality product when compared to the bigs. Think minor league baseball's pay scale:
Complex league: From $4,800 per year to $19,800
Low-A: $11,000 to $26,200
High-A: $11,000 to $27,300
AA: $13,800 to $30,250
AAA: $17,500 to $35,800