It's not just that we got good at dealing with triangles, it's that triangles are really easy to work with. I think the reason for using triangle meshes in 3D

It's not just that we got good at dealing with triangles, it's that triangles are really easy to work with. I think the reason for using triangle meshes in 3D printing is for the benefit of the slicer (or its developers) -- the slicers consume triangle meshes because that made building the software feasible. Your printer quite likely implements some amount of non-linear (as in curved) moves. Having said that, I'm sure I heard relatively recently about some slicers starting to support STEP input files or some other solid modeling format, but my searches just turned up "how to convert your STL files to STEP files" SEO trash, which is a bit funny.