I think the primary reason is because they are a simple design that is attractive. There are not many design candidates available that meet that criteria. A cutout adds to the overall impression of a frame. It suggests more effort and thought went into it and even appears to make the frame lighter (even though it doesn't really). It distinguishes and identifies a frame in a favorable way from it's less worthy competition.
When I was making my first frame in England, I put a lot of thought into what might make a nice cutout. There are not many options. I settled on doing a fleur-de-lis. While that design is not complex, it is tricky to get the curves and proportions correct in the small area available on top of a lug. Eventually I discovered how to put the owners initial in the down tube lug and felt that when everything else was plain and simple, it provided a nice custom touch. I cut them out with a jeweler's saw and files. I've gotten a number of saws over the years to do this task but my favorite was made by Eclipse that I bought in Bradford, Yorkshire, UK while I was learning.
Niles, Michigan, USA