Universities can and they do:

https://public.com/bonds/screener?issuerSymbol=PDFHV

The yield on ~20 year Harvard bonds seems to be about one percentage point higher than the yield on 20 year treasuries.

Those are standard, unsecured bonds. They're not loans against anything in the endowment.

Right, and the endowment already uses leverage, so many of the endowment's assets will already serve as security for loans.

Sure, but that's margin trading. These bonds have nothing to do with the endowment.

Yeah, sorry I didn't make it clear enough that I was agreeing with you. The endowment's assets are likely mostly/all pledged as security for margin trading, in which case there may be few/no assets left which could serve as collateral for borrowing that will fund payouts.

Or just use the endowment directly. Quick napkin math says that Harvard could make tuition free for all undergrads for 26 years with what they current have. Originally this money was meant to be spent on education but they just let it grow forever. Some of their hedge fund managers are approaching 8-figure annual compensation packages and I can't help but assume this is part of what has corrupted the university. Citadel LLC has $65 billion AUM, while Harvard has $53 billion while getting special tax-exemptions.