Why Doesn't Youtube Have A Repeat Button?
According to YouTube Video Marketing Services.YouTube pays uploaders who are willing to have ads featured in their videos based on the number of views they have.
So, if there was a 'repeat' button, they would need to design a system in which can tell if a video is actually being re-watched this many times, or whether it's a malicious tool used to manipulate YouTube views to get a bigger payout for channels who have vested interests in more views.
This would cause a lot of trouble on YouTube with creators, with new strict regulations in place - it would be an issue which Google's Adsense system would not want to expose itself to, but rather let third party services like YouTubeRepeat offer a 'repeat' service' since they still gain a view in this way.