Well....
What you say is certainly true, but you're forgetting about Science!
A theme of Fallout is science run amok, future shock, unchecked progress and technological advancement. Fallout's universe contains a seemingly unending supply of mad scientists. A common theme that pops up a lot is the concept of the scientist who is less concerned with the moral or practical implications of what they're doing, and more interested in the very fact of the research itself.
(In other words - "You ask why I would create a race of sentient and self-aware replicants to use as slaves when a robot without free will would make a much better servant? To you I say, because I could, therefore I must!")
A mad scientist isn't necessarily going to begin with a goal and then design something which fills that role. More... "likely" would be that you've got a mad scientist that created a bunch of androids and whoever it is that rules the place (possibly even the mad scientist I suppose) decided to use those androids as slaves. ie, a mad scientist isn't going to make androids specifically to be used as slaves - they're going to be making androids and leaving someone else to worry about what to do with them.
Of course that's obviously just rationalization on my part. It's basically the Blade Runner problem - clearly these things are more trouble than they're worth, and on top of you not being able to keep them from rebelling or going crazy but you've decided to make them look exactly like humans so that they're also nearly impossible to find. But the entire premise is based on that, and more important is the metaphorical imagery and allegory anyway, so what are going to do?