Well think about it. Imagine you had no alternative to getting any video on the internet? After all, if not youtube, anything else was probably slower at the time. Obviously you wouldn't simply lose the desire to watch relevant videos, it'd be dimmed quite significantly sure but you'd still want to watch a video every now and then. Whether it's a music video, or a chess match or a farming lecture, there's just a ridiculous amount of content available. I have plenty of videos I'd want to watch even if I'd have to wait hours. (take torrenting for example, or pre-youtube & pre-streaming file sharing, video and music on p2p networks were incredibly slow yet incredibly popular).

But if you couldn't even load the pages to browse through the videos, that'd pretty significantly reduce your watching even further.

Liken it perhaps to a library where you could only get 1 book per week. Well that's not much, but at least you can get 1 book. But if you go to the library you have to wait in line for an hour, and after examining one book section of 10 books, you have to wait 5 minutes to examine the next one. Choosing the weekly book would become such a chore you'd probably not even bother to go anymore. But if you'd suddenly be able to examine the entire library with only 1 minute of total waiting, many more would be much more inclined to do so, even if they could still only borrow 1 book per week.

Beyond that in my experience, lots of requests in a slow connection often fails before completing fully. I don't know why exactly, I've never been a network engineer. While streaming in a slow connection eventually gets there. So it's entirely possible that even browsing normal pages was failing entirely before for some people, even though (if they ever did load the page and choose a video), the video download worked fine albeit at a very slow pace.