I sell my products (not bath & body) at wholesale and I ask for a tax ID number when establishing a wholesale account with someone.
That information tells me the person is prepared to pay state sales tax on their sales within their state. Otherwise, I could be held liable for paying MY state sales tax on my sales to them.
It also means the person is more likely to be a legit business -- it weeds out most of the retail buyers who sneakily want to buy at wholesale. I get a few like that from time to time.
If a craft fair does not ask for ID numbers, then the fair organizers could be held liable for paying state sales tax on the gross sales from the show -- they can't prove their vendors are ready to pay the sales tax. So it's pretty dumb to not want that info from their vendors.