Same reason I can't easily start an AT&T/Verizon competitor.
Doesn't mean their pricing is that reasonable, or that funding education should be run this way in the first place. It just means there are big barriers to entry, often established by the existing players to protect their margins. The Fed rate for student loans should be lower.
edit: Yeah, that other comment is talking about European rates, not American rates.
https://studentaid.gov/understand-aid/types/loans/interest-r...
6.39% to 8.94%, and that's for Federal. Private ones tend to be even higher.