Yeah, it shares a codebase with the Windows 7 version if it's different at all. The number of Windows 7 + Windows 8 installs is far greater than Windows Phone users.
Youtube is considered core mobile functionality, like a browser, but Youtube is a fiefdom in which Google does not have to compete (unlike the ultra-competitive landscape of the Browser wars). While Google has nothing to lose and everything to gain from restricting access to YouTube, the same cannot be said about the Browser, thus they compete.
It's simple economics; don't waste money helping people dethrone your monopoly (I AM NOT ADVOCATING THIS POSITION, SIMPLY STATING MY PERCEPTION).