Why is YouTube not supported on the YouView box?
(I'd like to use it with my AV Amp...)
Because Youview is an retail platform, it would be up to YouTube/Google to approach Youview if they want to put their app on Youview. There may be technical or commercial reasons for YouTube not being available on any given platform.
For example, Google are on the verge of pulling YouTube from every Roku device in the world because they're claiming that Roku aren't being very fair and Roku are claiming that Google want to dominate search results at the expense of every other app and they also want access to all Roku viewer data to further tailor their search results to favour YouTube over Netflix etc....