It's not obvious why using the HTML5 API is "impossible". Windows bundles a <video>-capable browser; assuming IE's capable of playing either H.264 or WebM, it should be relatively easy to build a YouTube app on top of it. Maybe there's some internal reason why an app can't easily embed an IE widget.
[1] http://www.winrumors.com/no-flash-for-windows-phone-as-adobe...