Do kids even want their own horror movies? When I was a kid we just watched the r rated adult horror.
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Kids definitely deserve more horror flicks if you ask me.
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'Lady In White' has now got a 15 rating so it's definitely not family horror. Family horror can work for tweenies (9 to 12) but even then it needs to be mild. As you say the younger children can find all the scary stuff in Disney villains.

Why do little kids need gore or deliberate terror? When you are five, the villains in Disney movies are scary. Want to have your kid watch a scary movie show them Pinocchio. I have never heard of Lady in White so I looked it up. With its PG-13 rating it sounds more like a teen movie than a kid flick.
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I don't think it's so much studios' faults as it is over-protective parents who think their kids won't handle disturbing imagery.
is it bad if I sort of understand? I mean, if I were a parent, I wouldn't want to have to escort my screaming, terrified kid out of a theatre while the movie's still playing. Most young children tend to react to fear by acting loudly. I wouldn't want to disturb anyone else in the theatre's experience because my kid reacted badly to a jump scare.
I think it's healthy if a parent allows a child to grow up with scary content (like, showing them scarier animated Disney films when they're little, such as Pinocchio or Bambi, so that they're accustomed to scary moments in films) but many parents don't do that. They bubblewrap their kids and only give them "safe" content that shows absolutely no violence and minimal conflict. So, family-horror films are too risky, because many kids simply can't handle them due to over-protective parenting. Or, parents simply won't take their kids to them because they think that their children shouldn't be exposed to horror and violence.
Why does life have to be so ironic?!