While I understand and sympathize with your concern, calling it a violation of the 1st Amendment is disingenuous. The 1st Amendment does not, nor was it ever intended to regulate the rules and regulations of private organizations.
You are assuming the NCAA is a private organization. Courts have ruled this both ways, but there is at least a straight faced argument that the NCAA is a quasi-governmental agency. They do receive public funds from the government and the vast majority of their revenue is derived from government sponsored entities...mainly....public institutions.