In the earliest design stage of the game both strategic resources and luxes were not hooked up by great people improvements. But the problem arose that people had put a great person improvement on a tile where later a strategic resource popped up. Then they had an awkward choice to make, so the designers chose to give great person improvements the property of giving access to strategic resources.
With luxes there wasn't the same problem, because you see those from the start of the game, so it's possible to avoid placing a great person improvement there.
You could say resources like marble and ivory are both a lux and a strategic resource, because they are needed for buildings as well, but with regards to great person improvements they behave like a luxury.
