Cut-outs are more a vanity thing -- something the builder does to distinguish their frames from others.
Yup. Back in the day, plenty of high-end bikes had cut-outs and plenty of equally nice, expensive bikes did not. Had nothing to do with drainage (unless you submerge it, not much water can get into a built-up bike frame anyway). Some BBs came with sleeves and some didn't. Sleeves would help keep out dirt from the road if the BB had holes, but just as important, it would keep rust from the frame tubes & BB away from the bearings.
Also, track frames had BB cut-outs: here's a 1977 Cinelli track:
