It was really an eye-opening experience to go through a big list of these videos. Thank you to everyone who has participated. It definitely gives me a new perspective. I once thought it inconsiderate that YC didn't even click the demo link in my application, but now it's obvious that it's a necessary evil in sifting through so much of this.
One thing that stood out to me was how late all the videos were in the application process. About 75% of the videos were submitted within 48 hours of the deadline. It seems that submitting just a week earlier than the deadline would gain a huge advantage in terms of how much time the YC folks are able to commit to your application.
If I had to sift through this many videos in a short amount of time, I wouldn't even finish most of them. Whereas, if I received a video for the first time in a few days, I'd probably watch the whole thing regardless, and even try out the demo.