The original intention of Batman doesn't really matter to me since I don't read the earliest comics. The stuff I'll read is usually Bronze Age or modern graphic novels that depict Batman as a dark, more mature character. Where the villains are real sickos. Batman is BOTH a story for kids and adults. That's what it's become. Especially since the 70's/80's. I do have a personal attachment to Batman so even if he was just for kids, I'd give it a pass because I was a fan of Batman as a child. So that stuff carries over. As a 33 year old, I really don't think I'd latch onto a Spider-Man movie or comic these days if I was introduced to it recently. But because I experienced it as a child in the 90's, I can sit there and really get immersed in a future Tom Holland Spider-Man movie that may have childish humour and villains.
But Batman has become more than a kid friendly superhero. Wearing a costume does not mean it's for kids. That clown you talk about is basically a serial killer. And comics across multiple mediums have stories with those guys where the tone is very serious and tragic and horrifying. Grant Morrison's Arkham Asylum is for adults. Straight up. It's pure horror. If it was adapted it would be Rated R or a PG-13 rating that teeters on a R just like this movie we're all going to see in March.
So I simply don't see Batman the same way you do. It's kinda in its own category because the tone is so flexible. And my nostalgia and bias for Batman plays a large part in why I'm still even interested in this character, sure. But I can honestly say that if I only heard of Batman last year, I'd be intrigued enough to buy comics like Ego, Year One, Prey, ASHOSE, Her Sister's Keeper, Nine Lives, Night Cries, Long Halloween. A Superman comic? Forget it.