For dancing, thinner sleeves can better show off the dancer's lines, where fuller sleeves would obscure them. I've seen costumes in construction for a ballet, and they were supposed to be modern business suits. They had the highest armholes imaginable, like shirts. Some of the Astaire pictures have comparably high armholes, and I wouldn't be surprised if they were made expressly for making him look good while dancing.
+1 to that- I have friends that are professional ballroom dancers, and their suits fit like nothing I have ever seen anywhere.