I have not read all the messages.
but the correct answer is: to lower weight of the frame. it is an area where you could shave off a chunk of steel, yet still have a good sturdy bottom bracket joining your tubes.

as for the bearings, you should have a plastic sleeve to encase the axle and the bearings.

no, these were not limited to road bikes. track bikes had them too.
no, they were not "to let grease drip out".

maybe, they could be for water drainage, but not likely (except for frames with entry points, like holes in top tube to lower weight, cable-routing holes, etc.)

yes, to lower weight
yes, on a road bike, you would have a nylon (plastic) sleeve (some were very specific, some had accordeon style ripples, some were adjustable (2 cylinders, oneslightly conical that presses into the other)


Now... if anyone knows who made frames with an octagram bottom bracket cutout, some guy on FB would like to know (that is what I came searching for when it landed me here)