BATMAN comics had long used gimmicky ideas and outrageous situations. What the comics didn't tend to be was deliberately funny, which the show definitely was. My understanding is that Hugh Hefner was running the 1943 BATMAN serial at the Playboy Mansion, and it inspired such laughs that William Dozier thought it would be good to do something like that, and REALLY push the humor level.
Some time back I read an article about the SAM SPADE radio show, which starred Howard Duff, and was EXTREMELY popular in the 40's & 50's. It seems the longer the show was on the air, the scripts kept getting wilder, more outrageous, more hilarious. It was described as having an apparent influence on the later ROCKY & BULLWINKLE in its approach to humor-- you had a "serious" story for those who wanted it, but the dialogue had multiple meanings and was funny as hell. It could be enjoyed by several completely different audiences as a result-- which is how the '66 BATMAN show was when it started. (Of course, after the 1st year, it degenerated into a sitcom and any pretense of drama, suspense, mood, character, just fell by the wayside.)
Meanwhile... the '67 FANTASTIC FOUR cartoons were (along with the '67 SPIDER-MAN cartoons) my introduction to Marvel Comics. Despite the F.F. not having the budget it deserved, it still had a unique look and better writing than on any other Saturday morning cartoon show. Later I discovered this was because most (sadly, not all) of the stories were adaptations of actual Lee-Kirby comic-book stories, even using ACTUAL dialogue & designs here and there. I'm SURE it could have been even better-- but as it was, it was the best "advertisement" the books could ever have had.
My dream project, of course, would be to see an F.F. cartoon series where all of the Lee-Kirby comics would be adapted, one issue per episode, in sequence, with as much of the original dialogue intact as possible. If they can do it with Shakespeare and Arthur Conan Doyle, WHY NOT Lee & Kirby?