This is purely speculative but I hope is not removed because it would be a good point of discussion, but is it possible that there wasn't necessarily a dramatic increase in the number of serial killers, but perhaps because of advancements in forensic and other crime fighting technologies, that more people were being caught or discovered?
Out of interest, what is the assumption predicated on? Have there been any studies pertaining to the incidence of serial killers before, during and after than period? I imagine it would be difficult to determine how many serial killers were active at a given time considering how many such crimes remain unsolved, or in some cases uninvestigated.
William Strauss and Neil Howe's various works on generational cycles in American history explain the apparent violence of this period as a side effect of children 20 years previous growing up during a period of "declining protections" - i.e. less active parenting and guidance, more "latchkey" and "free-roaming" permissions, and a loosening of punishment in schools. They identify a general turning point around 1984 where protections start trending upwards again(consider today's environment: "zero tolerance" schooling, "helicopter parenting"). The ~8-year period between then and when crime figures start to decline is explained as lag time where the violent cohort is becoming more active even as a gentler generation is emerging.
Since the Strauss-Howe concept works from a top-down structuring of history, some caution around this particular interpretation is, of course, advisable; any number of sources can be cherry-picked to composite an image of a society that turns young people into serial killers. But the story it tells is ultimately about as persuasive as the explanations that correlate lead or birth control; one way or another, something about the environment at that time was making kids grow up more violent, on average - it wasn't a case of mild-mannered "Dr. Jekyll" adults suddenly turning into crazed "Mr. Hydes." There are lots of changes in the post-war period that could cause that. Teasing out which ones mattered is nearly impossible.
I wanted to add a question: how does massive media portrayal (news, movies, tv shows) correlate with the increase?
In the 1970s and 80s, we started to recognize that they exist and then also started talking openly in public about the subject with people making movies and books on the subject. Psycho did a lot to publicize them with many starting to be known by the public afterward.
We also had advances in forensic science and technology- fingerprints becoming digitalized in 1980, then being able to be spread on the intern to various law enforcement agencies
The development of forensic DNA testing in 1987 with the Colin Pitchfork in England in a DNA dragnet (this never could have happened in the US in this manner), then the development of a much easier sequencing technique with PCR by Kary Mullis. This developed into the CODIS program, which allows DNA profiles to be kept on file also by law enforcement agencies starting in the late 80s/early 90s.
The third piece is the body farm in Tennessee as run by Bill Bass and his group. This allowed for research to be done on dead bodies to be examined in all states of manner and decomp. There are some slight issues, but those are all technical and historical.
Even as these technologies were changing, the FBI started the serial profiling unit with John Douglas and a few others. There were some profilers and attempts at profiling in the past, but this was the first major development in a law enforcement agency internally (that I'm aware of). They made several key arrests with their successes being publicized a lot. I'm not crazy about profiling for a few reasons, but it's not without its merit.
But in the 70-80s, the media did a huge part in pushing serial killers into the forefront of our mainstream. It wasn't that they suddenly developed (HH Holmes is a good historic example), but it's that we suddenly became aware of them, had tools to catch them, and a media that played up their crimes as much as possible- books, movies, tv shows, movies of the week, Ann Rule, news reports, just an endless inundation of murder and sorrow. Ted Bundy might be the apex of serial killing, slasher movies, Stephen King, because he completely broke the pattern- he'd been sophisticated, smart, well connected politically, worked a suicide hotline, on and on, and then went on to kill a bunch of sorority girls. The media couldn't get enough. All of this made us, the public, much more aware of these things and also better at protecting ourselves. It's not that we are 100% protected, but that we've become more attuned to "What's out there and who might be out there." One quick example is that hardly anyone hitchhikes anymore, especially for women, even though that used to be a pretty common practice.
It's probably not that serial killers dramatically increased like everyone is trying to pin on lead poisoning, it's that we were suddenly aware of them, have a media who thrives on them, and new technology has been developed to stop many from getting crazy out of control and are able to be caught earlier in their practices.
This doesn't include the "smarter" Ted Bundy-Dexter types who know how to cover their tracks better, or grew up in a post CSI-OJ Simpson world where they know about DNA and fingerprints.