[Animats]

Most of those problems are associated with small domes. As domes get larger, the edges get closer to straight and many of those problems go away.

Large domes are usually built with only the top third of a sphere or less. This generates huge outward stresses at the base, so there's a steel ring in tension to support them. This works fine. Often the outer walls are raised, so the dome doesn't go all the way down to the ground. This allows roofing a big area with a sturdy structure.

Syufy Theaters built many domed theaters around Silicon Valley. The original ones were radial, not geodesic - radial beams tied together by ring beams. The Houston Astrodome is a similar design. Although vacant and unmaintained, the Astrodome is holding up well. Later Syufy went with octagonal buildings, such as the Century Cinemas next to Google HQ. This kept their round branding, but allowed better subdividing into multiplexes.