Except that, as I said, the Batman and other DC comics of the day weren't played straight. They were full of deliberately goofy, zany, ridiculous situations and sitcom-like character plots. There's no way the writers who came up with the likes of the Rainbow Batman weren't trying to tell funny stories. The reason the producers of the show made it a comedy is because that's what the comics already were.
You are right, but a lot of the stuff you mention was jettisoned from the book two years before the series was made. DC was trying to bring Batman back into something resembling reality with the "New Look" because sales had dropped so low, they were considering killing off the character. Julius Schwartz took over and restored his status as a great detective and dropping the aliens, Bat-Mite, time travel, Ace The Bat-Hound and others. They even killed off Alfred and introduced Aunt Harriet (who was not created by the producers of TV series no matter what William Dozier said). Alfred returned well after the series was on the air. While the book was still fairly lighthearted, it wasn't the wacko sitcom it used to be.
However, the TV series was
more in line with the New Look (no aliens, Bat-Mite and the rest). The comedy was in the exaggeration of the dramatics and the colorful characters. They just made the good guys impossibly square and virtuous. That was actually the biggest change from the comics; for example, Commissioner Gordon in the comics was not as "constipated" as the TV series version (I got that reference from a book because I couldn't come up with anything on my own that was as dead on accurate). The BIFF! POW!! stuff was funny because it was not something you'd see on TV. Real sound effects do that job, and it wasn't still later they goofed around with them for humor (WHACK-ETH!).
So, yes, you're right, they reflected the comics of the day, just more over the top. Unfortunately, DC let the series comedy spill back onto the comics. They themselves didn't get the joke and could have left Batman as he was and people would still have enjoyed it. They let the TV series hamper Batman's return to something more serious and he stayed campy until Denny O'Neil and Neal Adams took him back into the shadows.