I never had as much problem with the "generation" bit as with the "one girl in all the world" bit. If we accept the fact that there are demons of some sort scattered throughout the world, the Slayer population seemed a little scarce. Of course, in defense of the Shadow Men, mankind was probably limited to a small area during their time, and they either didn't care about the demons anywhere else or just never thought that far into the future. The modern post-Chosen arrangement seems more logical when thought of that way.