Is it just that the costs of serving video require an enormous company or is it that the term youtube is basically synonymous with "internet video".
Before Flash video, before html5 video, video was very difficult on the web to make work, the small yet pretty good codecs that the flash player video had were revolutionary at the time (Back in Macromedia days). Flash compression was always one of the best even though it was mostly software, still swf files are compressed/streamed in a very compact way.
Those specifically timed events won't happen again the same way, Youtube was born at the cusp of social media and the technology that made video economical enough. Youtube wouldn't be known as it is without that Flash video moment in history.
There are other alternatives though, dailymotion.com is fairly popular and will accept anything.
The front page of vimeo isn't as good though. It tells you about vimeo itself rather than giving you a large search bar and a bunch of content like youtube does.
I think it doesn't get used as much though because they will pull content if you're just posting videos of your friend doing cartwheels or something. There is a higher barrier to entry but they also only want very high quality HD or serious commercial or educational content.
I wonder whether they aren't more forward about discovery to save on bandwidth money.
Vimeo really needs to step up their mobile game.
If they couldn't do it, it's unlikely anyone else can.