For HTTP/2 at least, I think the main benefit in terms of performance applies to the "last hop", so you still get a more reliable experience even if the connection between the CDN/proxy and app server is http/1.1
True, through many web-sites don't have to care about the performance difference.
But for companies like CloudFlare or Googl HTTP/2 means less traffic overhead (multiplexing+header compression) and can save them a lot of bandwidth (aka. money) with that.
But for companies like CloudFlare or Googl HTTP/2 means less traffic overhead (multiplexing+header compression) and can save them a lot of bandwidth (aka. money) with that.