But would American viewers be interested in a show about an advanced human saving Earth from nuclear disasters brought on by human race?
The nuclear disaster was just the premise of the first episode. According to the series pitch, stories could've been about any number of different things. They could've been about taking on the Mafia or the Kremlin, or catching a modern-day Jack the Ripper, or preventing a dangerous experiment from going awry, or something on a more personal scale like keeping a young scientist from ruining his life before he could make a great breakthrough.
And like I said, The Man from U.N.C.L.E.
was a similar premise; the U.N.C.L.E. was an international organization dedicated to defending against threats to world peace and stability. And that show ran for four years, albeit mainly on the charisma of its leads.
As for Gary's advancement, the pitch document specifically addresses whether his superiority would be alienating to viewers, and argues that audiences actually responded positively to "superhuman" characters like Spock or James Bond (or Have Gun -- Will Travel
's Paladin, who, again, was Roddenberry's template for Gary Seven).
I also think that by canonizing G7 as a time-traveler, it opens doors to have him show up elsewhere in Trek, which I think Trek fans just want to see happen, regardless of Gene's original intention. Since the series didn't happen, he can (in theory) be an occasional guest star elsewhere, which is interesting to ponder.
Sure, and that very thing has been done in the novels and comics, and I've personally drawn on it in my own Trek fiction. So I've got nothing against taking the character in that direction in the context of Trek tie-ins. I'm just pointing out that there's a difference between that after-the-fact fan interpretation of the premise and what the creators of the show actually intended.