in my defense, I was going off the top of my head. But, yeah, especially Batman and The Shadow crossed paths a couple of times going way back to the 1970s, so I should have thought of that.And Doc Savage and the Shadow as well.
Surprised that neither Zorro nor The Phantom (The Ghost Who Walks) have crossed paths with Batman yet, as far as I know. Or Carl Kolchak.
With Zorro and the Phantom, I think their comic book licences* have bounced around a bit too much, they never stayed with a publisher long enough for them to knock on DC's door. And to be fair, since Frank Miller, Zorro has kind of been part of Batman's origin.
As for Carl Kolchak, as much as I'd love to see more of him, there have barely been any comics with him around, anyway. I know Moonstone did some comics with him, but in the past few years, they seem to have focused on novellas and short stories for that character. But those tend to be really good, so I wouldn't want to see the licence go someplace else just to get a Batman crossover.
Thinking about it, a Batman crossover really only would make sense in that period post-Zero Hour until War Games when Batman's existence was treated in-universe as an urban legend. What could be great would be Carl Kolchak investigating Disney's Gargoyles.
*Zorro should be public domain by now, no? But I guess they can't put his name in the title because there's still a trademark. Same reason the unlicenced comic adaptations of the public domain Conan stories are titled The Cimmerian.