I think the issue is that a lot of family court stuff is so very, very specific it would identify children to a much wider extent than most rape trials do. It’s also how far would you go with the reporting, an awful lot of abusive partners absolutely slate the tit out of their partner/ex via family court, so opening them up opens up more avenues to use that as abuse too.I've always said this. If we can keep rape victims anonymous in public criminal courts there's no reason to not have the family courts opened up.
There are sometimes (in England at least) full reporting restrictions on rape trials, generally where the victim is related to the rapist for the same reason - and if it is reported at all then they’re not allowed to name the rapist. Which is really the closest analogy to family court.