The thing with Smith it was both the reason it was successful AND the reason why it jumped the shark. The same could be said of Fonzie overtaking Richie on Happy Days (which led to the term jumping the shark in the first place). For a half a century now fans have theorized what heights LiS might have reached had it stayed more serious. I think a big part of the appeal of that is it remains a figment of people's imaginations and not something we ever saw. Fantasies are always better than reality.
One Irwin Allen show that stayed serious was Voyage to the Bottom of the Sea. Even when it was silly, it was played straight, and I think the end result comes across as a little flat, like a stereotypical horror B-movie stretched into a series. LiS early episodes have a similar vibe, only softened with an overlay of wholesome family values. The injection of humor from Smith and the Robot--up to a point--helped add warmth and whimsy to the show. It's all about finding the right balance.
The thing is, there's a difference between being humorous and being campy -- and between good camp and bad camp. The show had already moved toward a more humorous interpretation of Smith by the middle of the first season, but it was still vastly better than what came afterward, because it wasn't camp yet, just humor. They already
had the right balance you're talking about, but then they lost it in season 2. In an attempt to compete with
Batman, the second season embraced extreme campiness and absurdity, and it became awful as a result. It's not about humor vs. seriousness; it's about changing from a style of humor that worked reasonably well to a style of "humor" that was just obnoxious and stupid. The mistake they made was trying to copy a different show's approach, which rarely works well. Both LiS and
The Man from U.N.C.L.E. adopted a campier approach in their 1966-7 seasons in an attempt to copy
Batman's success, and both did a poor job of it and suffered in quality as a result. They compromised their own voices and identities and failed to capture what worked about the thing they were trying to imitate.
I think the reason
Batman's campiness worked was because it was anchored in something specific and cohesive -- it was a rather faithful representation of the storytelling style of Silver Age comic books, playing their tropes so literally and with such exaggerated seriousness that it became absurd. But since it was reflecting a real, ongoing genre, that gave it structure and focus. Its absurdities were largely based on specific tropes from the comics, and from the '40s movie serials whose revival inspired the creation of the show. It also had a fair degree of satire of things going on in the real world, like political campaigns and pop art. But LiS's camp was more unfocused. It was just whatever random nonsense the writers thought up as a catalyst for Dr. Smith's antics. Perhaps if they'd picked a specific genre to lampoon and pastiche -- say, if their writers had been familiar with pulp sci-fi and monster comics and had done the show as an exaggerated spoof/satire of those tropes -- that would've given its absurdity more focus and purpose. The camp would actually have worked the way camp is supposed to work, as a send-up of some kind of establishment or convention. It would've been more than just random inanity.
