Workaround: Use the desktop site, here is how:
- In mobile Safari, find the clip that you want to watch, it will
initially start in low resolution.
- Tap the address bar.
- Swipe down in the page and you should see Request Desktop Site,
tap it. Sometimes this may open the clip in the YouTube app on the first attempt, try again!
- On the second attempt it may ask you to open in YouTube app, don't
- On the third attempt you should see the Desktop version of YouTube.
- Tap inside the video to start playing in HD, sometimes you need to tap a second time.
Note: on my iPhone 4s iOS 8.1.2 the Desktop version of YouTube is much slower, unresponsive and harder to use. But since YouTube app can't play any videos over AirPlay, I had to find alternatives.