If there was some redeeming quality about that old show, something akin to how the Original Trek had a good ethical message or some such, I'd be much more accepting of it.
The fact of the matter is though, it's a cheese festival of nonsense. The only argument in it's favor is from the point of view of childhood nostalgia.
Yes, Batman may have been campy in the comics for a long time. But such was due to the society in which comics had to be published, not due to design. You couldn't have a dark and gritty comic in the 50s. Or on TV in the 60s.
The characters origins speak for themselves. A child orphaned at the age of 8-to-10 by a lone gunmen who robs and shoots his parents right in front of him, who grows up to pursue justice and, frankly, vengeance. That isn't light hearted. It simply couldn't be done justice for a long time.
It's just like the old Battlestar Galactica compared to the new. A show which in 1978 couldn't do the premise of a rabble of survivors fleeing a mass holocaust justice. Come 2003, boom. It gets done right.
Every argument in favor of the campy Batman, or the campy Galactica, or anything else campy for that matter, is based wholly in childhood nostalgia. In recapturing the wonder of something enjoyed as a kid. Not in a logical or reasonable argument of "campy is superior because A, B and C" or so forth. The only time camp is good is when you're a small kid and can't handle reality as well.
People want to remember the 60s show fondly? I can't (nor would I) stop such. That's everyone's right, to recall something fondly from childhood. I have such things. We all do.
But at least admit, it's a pale watered-down imitation of the character that existed because corporate big-wigs didn't think people, especially kids, where sophisticated or smart enough to deal with actual drama or any sense of reality.
I don't think anyone is denying that Batman is at its best when it's done seriously. What everyone is trying to say is that despite that, the 60s series has its entertainment value. It's not really a wart of pimple of the Batman franchise, just another aspect of it. A popular one too.
There are a lot of people, even today who think of Adam West as Batman, and identify with the 60s series when they think of Batman. This clearly hasn't hurt the franchise as indicated by the ticket sales of Batman Begins, and The Dark Knight, as well as the hype building up for The Dark Knight Rises.