Americans (even some center-left ones) hate the idea of directly supporting anything, so cheap loans were used as a substitute for directly operating and funding public colleges. Same with housing.

Directly supporting people is "socialism," a handout, and is seen as supporting laziness and vice. A loan must be paid back, which allows many Americans to view it as something encouraging responsibility and virtue. It all comes down to the puritan work ethic.

The problem is that government backed loans are just an indirect way of giving welfare, and a monstrously perverse and inefficient way to boot. It drives price inflation which gets captured by the vendors of the products/services in question (existing home owners, builders, universities, etc.) instead of those you're trying to help and it creates debt bubbles that represent a danger to the overall health of the economy.

Overall it's probably worse than doing nothing due to the price inflation it generates. Housing was reasonable across much of the USA prior to the 'oughts. The housing bubble destroyed home affordability, an effect which as I said persists to this day.

Wouldn't directly supporting people also produce price inflation?

Yep, what the parent commenter didn't say was that pumping money into any system almost always results in prices going wayyy up to absorb the new demand. This happens regardless or whether it's loans or direct subsidies.

I believe the way laws generally deal with this is to only allow subsidies when the price is under some cap. Sadly we (or the US) don't do this for education it would seem