I didn't mean generation as in "a descendant of a previous anointed one", I was just referring to the fact that an anointed one would probably be replaced by someone from a younger generation because they likely "strayed" after some years, probably not after 2 or 3 years.
So if you imagine that the 1st century Christians populated the 1st generation of 144,000, and maybe the 2nd as well, and then things got corrupted and there were no anointed until Russell's time, you have about four generations of "true worshippers" up until now from which to keep picking replacements as a previous anointed one loses his appointment before "finishing his earthly course".
I wasn't aware that this explanation was ever formally rejected by the Society. As far as your assertion that the numbers would have to remain level or drop in order to support this theory, that would only be true if all rejected-and-replaced anointed ones ceased partaking.