"Donations to fund FA, or a building, or endow a professorship may serve some public interest, but donations to endow a coaching position? What public interest do they serve? Should they be tax-deductible, especially with donors receiving valuable benefits in return?"
Agreed. Time for these schools to separate athletic donations from legitimate charitable purposes.
Except all cash is fungible. The $1M I donate to sponsors Hanna's Varsity Handball team is $1M less than H has to spend out of general funds to support the Handball team, so they can spend $1M elsewhere.
However, if the handball team is over funded with donations restricted to it, the excess money cannot be used for other purposes.