I'll be blunt here: UDID or IDFA or a rabbit out of a hat, whatever, it still needs to be sent, so it uses up bandwidth same as a cookie.
If your point is that its size is smaller than typical cookies, then you should be advocating responsible use of cookies, just for a small ID, instead of their complete replacement.If your point is it is limited to only some requests instead of all requests, the same can be accomplished with cookies using cookie path or different domains, if needed. My oppinion of the situation is that it isn't needed - provided that the previous point is addressed - no matter how many requests you make, 20 bytes more or less is not important. But if you disagree, you have a solution with cookies, without reinventing the internet.
EDIT: Also, lets not fool ourselves here. UDID and IDFA and whatnot are not being introduced for the purpose of keeping a session within a single website. They are intended for tracking you across multiple sites and they can all die in horrible pain along with their creators and supporters as long as I'm concerned.