Sure, we are all allowed to have opinions, but he MUST be one thing. Right. Got it.
It is more accurate to say that the modern comic books are divergent from both the TV show and other comics. Batman... has not always been serious stuff. Dark, broody, of-questionable-mental-health-Batman is not the only Batman.
Sure, there's been detective Batman, vigilante Batman, patriotic Batman, and "Punisher" Batman. Despite your examples, however, there has really only been one consistently silly Batman and he was silly for adults, not kids. The covers don't really give away the story.