Too complicated, the easy explanation is one of the parents killed her, maybe on accident (punishment gone wrong), maybe on purpose (serious perversions I’d rather not contemplate). But there’s no way other than an inside job they could “search” the house multiple times and not find her, not to mention the absurdity of the multiple page ransom note written on site. The parents simply had to be involved, either that or the criminal was ridiculously brazen AND lucky the household found a way to sleep through the whole thing.
I think JonBenet died accidentally, perhaps from horsing around with her brother, and the parents flipped out and tried to make it look like an abduction/murder. My guess is that Patsy wrote the “ransom note” in an attempt to cover their tracks. But with Patsy now deceased, unless the father or brother talk, the whole story will never be known.