If you could only afford to own one general-purpose intelligent robot (I'm assuming that by far the most expensive part would be the brain), you'd want one that was approximately human in form, so it could operate tools and machinery intended for humans.
A human-shaped robot should be able to drive your car, use a pair of scissors, climb a ladder to clean the gutters, use a lawnmower to mow your lawn, use your vacuum cleaner to clean your carpets....ect.
Good luck trying to get an intelligent robot-car to to clean your gutters or bring you breakfast-in-bed!
ETA: But I suppose you could have one central robot-brain in your home which wirelessly controls purpose-built non-humanoid drone robot-bodies, such as a robotic lawnmower, ect. But the cost of getting separate remote drones for each specific task might be prohibitive.
ETAA: If you were talking about robots that could pass for human instead of merely humanoid in form, I guess it would effectively be a way for people to own the equivalent of loyal slaves and servants, without coming up against laws about human slavery or having to pay wages. A lot of people might want that.