Safekeeping, offline viewing, producing derivative works (it's great they allow setting CC licenses on videos, but are subsequently hostile to anyone trying to actually use those rights), and viewing on platforms where the browser or player doesn't work (that's been a few years by now though, now that all my hardware is newer and I'm no poor student anymore).

A great example I recently saw is someone extracting the audio feed and double checking the Doppler shift of a passing quadcopter to confirm a speed claim. It checked out and the math was included. Stellar comment. Harder to do if obtaining the video's data is made hard.