Earlier quoted context omitted.
.obj files don't hold any material information. When you check "Write Materials" in the obj-exporter properties (should be enabled by default) it will also export the materials to a separate .mtl file and reference them in the .obj file. Edit: see also here: https://en.wikipedia.org/wiki/Wavefront_.obj_file#Material_t...
That's a very straightforward extension to add, and if Blender does it, its popularity will ensure everyone else picks it up.
https://blenderartists.org/t/objs-and-mtls-how-do-you-work-w...
Most artists don't really seem to work with OBJ anymore anyway, it's an ancient format. I only use it when working in conjunction with ZBrush. Most people have moved onto FBX (especially for rigged meshes) and glTF is the new format that supports way way more:
https://www.youtube.com/watch?v=6IWKWT_2_Ls
https://forums.unrealengine.com/development-discussion/conte...