A chance he hasn't taken to this day.
The only person who really believed in the show was Gene Roddenberry, the creator of Star Trek, and when I say "believed," I mean "believed" with a capital BELI for "Beyond Excessive and a Little Insane." As executive producer, Roddenberry told the writers that, in his vision of the new Trek verse, interpersonal conflicts no longer existed.
Everyone on the show was supposed to act and feel like this great big family full of love, sunshine, and Tribble farts, even if that made it impossible to write drama. Ironically, the writers who had a problem with this were promptly told to live long and prosper in another job, while those who stayed had to sit around and discuss Roddenberry's ideas about sex in space, so who was the real winner here?
The staff's therapists?
While working on TNG, Roddenberry was reportedly suffering from brain disorders, diabetes, high blood pressure, and depression, which ultimately culminated in a stroke in 1989 and his death in 1991. It's easy to see how his condition could have influenced his fanatical behavior while developing the series. For a man in rapidly declining health, it's not unusual to cling to an idea of a utopian future without lust, greed, or conflict after realizing he probably won't live long enough to see it happen for real. Still, by the end of the third season, Roddenberry's tyrannical grip on the scripts had purportedly caused 24 writers to quit the show out of frustration. Or maybe it had something to do with the unbearable stench caused by the new TNG uniforms, which apparently smelled worse than the inside of Shatner's girdle.