Used to work for Vimeo, I know a bit about this.
Hosting videos is a non-trivial thing. Let's say you upload a video in 4K. Not everyone can watch in 4K, so it needs to be converted into other resolutions. That's transcoding. Then those other files need to be packaged so a player can intelligently upscale automatically depending on throttling — that requires a bunch of frontend and backend code to work correctly.
Instead of building it themselves, Cornell could pay $$$ for a white-labelled third-party service, but they would be on the hook for a large recurring cost, and they won't get the benefit of YouTube's excellent discovery.
We saw this phenomenon at Vimeo, which offers all the transcoding and throttling etc. Back in the day camera reviews were overwhelmingly hosted on Vimeo (mainly because it had a reputation for higher-quality video).
We assumed that paying users would prefer their videos be watched in isolation from others' accounts — this seems obvious, but it means that the average user watches fewer videos per session, which decreases the overall view count.
Over time YouTube mostly caught up on the video quality front, and camera reviewers were drawn to YouTube where there was a much greater chance of their video racking up a high view count than on Vimeo, simply because users watched more videos on YouTube.
Stated cynically, YouTube doesn't respect users' attention spans as much, so it gets more viewers' time than other platforms. That means more people want to put their videos there for people to watch.