I think I had asked this question a very, very long time ago and there were no certain answers.
In 1969, NBC was working with a lot of packagers (HQ, Stewart, Merv, Ron Greenburg, etc.), and at that time, G-T really wasn't coming up with anything new -- just revivals of older shows (save He Said, She Said). Perhaps that had something to do with it. Revivals weren't big at the time.
Within a few years, CBS had Budd Grant at the helm (he eventually moved up to be head of CBS Entertainment in 1980), and Grant wanted to get rid of the reruns (whether for cost reasons or not). By that point, The Lucy Show had been running in daytime for four years, The Beverly Hillbillies for six, Family Affair for two. All of these were "old-style" CBS shows, which they were getting rid of at night -- so no surprise, I suppose that daytime was the next to lose them. G-T was one of many packagers CBS was working with -- it seems they kept going back there because G-T was consistently successful with almost everything (Now You See It was their only miss over the first four years, and even that wasn't a bomb). Grant had also wanted to get Password back, but ABC beat him to it.
I don't know if Lin Bolen had any particular dislike of G-T; maybe CBS and ABC were getting first cracks at everything. It seemed, however, that Bolen wanted everything to look "new" and "hip," and maybe G-T didn't fit that mold as far as she was concerned. (This doesn't explain the Name That Tune revival.)
Anyway, Bolen and Chuck Barris got into an argument during a rehersal for The Gong Show according to Confessions of a Dangerous Mind, but Barris knew that her assistant and later successor Madeline David loved the concept (in fact, it was her idea for Barris to host after John Barbour was dismissed). I think Chuck had about worn out his welcome at ABC by that time.
By early 1978, when CBS and ABC settled a huge chunk of their schedules with soaps (almost all of which are still around today) and NBC was flailing, they went running back to G-T.
In other words, I have no freakin' clue.
EDIT: Lin Bolen was gone by the time The Gong Show came on, as you might have guessed, and Stumpers was part of the settlement. She also executive produced a prime-time show, W.E.B., in 1977, for NBC. She's not universally disliked (when I talked to him, Jim MacKrell sang her praises), and she still keeps an eye out on things (she wrote me to criticize my Jeopardy! page one day and praise my Celebrity Sweepstakes page the next, not connecting the two).
