And could variable diameter be of practical use in antenna design?

Tapered elements are common used in HF. They tend to load the antenna a bit,
thus shortening it. Some BW increase results as well.

At the other extreme, a continuously inverse- tapered antenna is quite broad in
bandwidth. Thus the Oliver Lodge, or 'bowtie' antenna, from 1897.

Old, old stuff.

73,
Chip N1IR