https://somethingaboutmaps.wordpress.com/2022/11/14/the-unnecessary-peril-of-the-fuller-projection/ is really unfortunate; I think the Fuller projection is useful and should be used more seriously.

I do suspect that you could find better projections on similar principles by (practically) exhaustive search of polyhedron rotations on Earth’s landmasses.

https://medium.com/vis-gl/unfolding-the-earth-myriahedral-projections-in-webgl-6b2bcfd00a30 goes in that direction and I think its octahedron is already arguably better than Fuller for its simplicity.