iTunes on Windows RT?

So, I've been thinking that Microsoft need to nail this one, and make W8 (even on ARM) a full desktop operating system. Now MS cronies throw words like that around all the time, so this is what I'm getting at; If I get a Surface, or some other RT Tab, I don't want to touch another PC again to 'set it up'.

One of the things I might conceivably need then is an RT App for iTunes. Will Apple protect their influence on digital music and decide to make one?

The more critical amongst you might throw this back at me with a suggestion that I should use Xbox Music or Spotify. I know, so try stick to the question.

Is it in Apple's interests to bother with an iTunes version on RT? I believe most iTunes downloads have been/are being run on Microsoft PCs and not Macs, so will they see the idea of consumers running an iPhone or iPod 'off' their WinRT Tab (using iTunes) as a good opportunity or try to ignore it completely?

Are these companies going to support each other given that neither really needs it? For example Microsoft are poised to release Office for iPad and Android soon, whereas Apple ditched Google even a year early to shove underdeveloped Maps on everybody, with amusing consequences.

In this paragraph, you'd probably expect me to sum up why the question is so important and paradigm-defining, but we know it's not, just a little interesting

And if it turns out they've already done one and I'm being stupid, let me know.