The uneven-but-mostly-OK post-apocalypse show Jeremiah (http://en.wikipedia.org/wiki/Jeremiah_%28TV_series%29) dealt with this problem in a better way: the Apocalypse MacGuffin was a disease that killed everyone who had been through puberty. The show was set 15 years after the "big death", so the characters were all people who had been too young to understand how these things worked when they were still working.

(Some were smart enough to figure the basics out, of course, which made them highly valuable.)