> I never dove into the subject enough to figure out if this plane representation was also internal to the compiled bsp format, but I suspect it is.

Not exactly. The BSP format stores planes as a normal (3 floats) + distance to the origin + an int that flags axis aligned planes. Which is the representation the engine uses.

I believe “3 points on the plane” was chosen for the map file so the coordinates could be exact integers in the text file, to avoid precision loss from storing the normal+distance representation. The latter representation uses less space and is easier to work with.