@Sybren A. Stüvel (sybren) seems you missed one of my previous message( message before I sent a file), I have answered on your question already. Thanks. If it is still unclear , I do not have a clear specification of how NURBS curves and surfaces should be written.
But please reread my long answer if you missed it.
I have tested it in last 2.83 and 2.9 (hash: rB83304e4c221b) builds . It still have this problem.
Check file I have sent before.

1. run 2.9 version. 2) select curves 3) export it in alembic format. 4) import that alembic file back to blender . Some of the curves types are broken.(nurbs curves are fine)

I think it is not correct to look as an example always on cube. Here is I did some comparison on more real examples.
For me in 90% rebuild subdivision works better then apply base , it try to be more close to high poly model then apply base. For example look on lips - in apply base lips getting too much close to each other and overlapping too much.

Unfortunately I do not have a clear specification and I do not understand the technical nuances. For my self I found solution to use only blender NURBS and create more vertices in it- then it works fine. But never export Poly or Bezier curves - then maya(version 2018 and 2019 ) crashes. Houdini 18 not crashes, but does not see Poly or Bezier curves correct. For Houdini the same solution - create blender Nurbs and add more vertices to it. Hope it will help somebody.
@Sybren A. Stüvel (sybren) I can only say that maybe we can convert and exporty Poly or Bezier curves the same way as NURBS curves, or convert it to NURBS before export.
For some of this bugs even no need to check it in other software - just export from blender and import it back.

I also have this problem. Blender 2.83

System Information
Operating system: Windows-10-10.0.18362-SP0 64 Bits
Graphics card: GeForce RTX 2060/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 442.19

any chance it will be in 2.83? It is pretty useful feature