Excellent question, Rambozo... You might ask that question in the luthier's section of the acoustic guitar forum as those guys might have a really good answer for you. Here, perhaps
@Christopher Cozad or
@AcornHouse might have one as well!
(3 weeks later...) I was sleeping.
I wish I could contribute something brilliant to the thread that has not already been said, specifically based on experience. I have never built an acoustic guitar using Birch. Kitchen cabinets? Yes. Stringed instruments? No.
I am already *that guy* that builds guitars using woods that are perhaps less popular. I tend to rely more heavily on so-called domestic woods that are readily available and the boards are large enough to minimize seams (Walnut(s), Maple(s), Myrtle, Cedar(s), Redwood, Spruce(s), etc). But there are many more domestic woods that can be (and have been) built into outstanding guitars, such as Alder, Oak, Ash, Osage Orange, Locust, Cherry, Pear, and Mulberry.
Like the author in the article Ralf mentioned, I have found highly figured Birch, such that I would want to feature on a guitar, to be less available. Of greater concern (to me), and echoing text already written, the typical size of the trees (and the resultant dimensional lumber that comes from them) tends to preclude me from using Birch for guitar backs - the boards aren't wide enough for my liking.
Others have already pointed out (and rightly so) that the majority of factories are selling into established markets, to established customer preferences (that the factories largely established, by the way). I suppose if Taylor were to heavily market a new line of Birch guitars ("Street Birch"? - Hey, don't laugh, it worked with "Urban Ash") others might follow.