I think the most undebatable benefit to oiling clay chips is that it deepens the colors. I don't know how many of us want a "glossy finish," I know I don't. Some people also say that when you oil a clay chip and it's "pores" are filled up with oil, it is less likely to get stained and easier to clean. I've oiled clay chips and can't say I have any opinion about mineral oil's protective capabilities.
I shouldn't comment on oiling china clays because I've never tried, so I'll just say I've very skeptical. China clays are much closer to plastic than clay, presumably less porous, and I have a hard time believing the oil does much but sit on the surface of the chip.