I remember reading a story in Analog science fiction about just this scenario: inexpensive, multi purpose robots (and the riots they caused when people realized they could be replaced).

The solution? Have each robot owned by one, and only one, human being, who could lease out the robot's "labor" as they wished.

I doubt that solution is possible, but I do think the issues the story raised are going to be, as you put it, "the biggest story" of the near future.

(I wish I could remember the name of that story!)