Slaves are individuals that are forced to obey the will of their master by the fear of being killed or otherwise punished. The reason to have them is that it is easier than using free people for the same labor. Reasons might be economical (cheaper) or circumstantial (job too demeaning). Now, once you purchase slaves, you have to be on the lookout so that they wouldn't escape. You must either have lots of trained guards, carefully designed slave quarters, and experience in tracking down run-away slaves, or you must have broad public and political support of the institution of slavery. In the later case, interested parties will take it upon themselves to make sure a run-away slave won't get away - otherwise the system wouldn't be very effective.
Do you see any of that in Fallout?
There also appears to be very little effect that slaves have on places where they are seen. Vault City wasn't built by slaves, neither is New Reno famous for slave girls. In fact, the effect is quite transparent. Now normally that would be perfectly explained by jet experiments and Enclave, except that if you remember the one ending slide of FO2, slavers prospered long after the fall of the Enclave and Vault City, and jet experiments can't support that demand.
There is a possibility that I haven't considered, however - NCR appears to be quite tolerant of the slavery. It's possible that the Republic ranchers are indeed using quite a lot of the slave labor, but then there's the Rangers who operate quite openly against slavery, and the game doesn't really show any slaves working at Westin's farm, or otherwise give any hint that supports the theory of legalized slavery in NCR.