A lot of this may be because people who get into Ivy League universities are (rightly or wrongly) seen as talented and hard-working. Most people don't have qualms about money going to talented & hard-working people who are down on their luck; they have qualms about money going to lazy mooches who'll spend it on booze.
Now, whether it's true that Ivy League student = talented & hard-working and welfare mom = lazy hedonistic mooch is another discussion, but those are the stereotypes that many people operate under.
Misaimed. The money doesn't go to the ivy league student. It passes directly to administrators, professors, etc, via tuition and endless fees. The more expensive the school, the lower percentage the kids get to skim off for living expenses. So at vo-tech level most of the money loaned as a percentage is going for booze, apartments, cars, gas, food rather than tuition.
Now if the kids got huge loans, stuck the dough in stock market funds, defer interest until graduation at which time they cashed in the funds, paid taxes and paid off the interest free loans, and kept a tidy small profit, as my econ professor and his friends did in the 70s/80s, then money could be said to go to the kids. This practice has been pretty much eliminated.