There is some logic in using the expression, although the word "platform" itself doesn't really seem to fit. The word "system" may be a slightly better word but even that isn't quite right.
You may recall back in the 1960s, there was an attempt to create a small arms weapon system, a modular weapons system to be exact, with the Stoner 63. The idea was to be able to create multiple configurations of a 5.56mm caliber small arms to include light machine gun, rifle, carbine and more variations of the machine gun. In theory, it sounded like a good idea and numbers were produced and used but I suppose it was too late on the scene. I also understand it wasn't exactly perfect, which could also be said of other weapons which nevertheless continued in use.
In the case of the Stoner 63, it looks like the only common parts were the receiver and the gas system, there being different barrel lengths. There were different feeding systems but they were all basically the same gun. I'm sure there are other examples but I can't think of any at the moment. It might be a case of the advantages that were the selling points weren't really much of an advantage after all, especially if it wasn't reliable. It was like the gadgets you see people selling at the state fair. It slices; it dices.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.