Sometimes children are better off in the home where there mother controls what they experience to some degree than at the whims of an abuser alone for 50% contact time.
Courts see 50/50 as standard and to be honest, if this was the future reality for my daughters then I would still be in my relationship.
When all at home together, they maybe dealt with 10 or 20% time where he was around with them, even less if he worked overtime.
With contact which is unsupervised they are alone with him, for much more time as he wouldn't now choose to do so much overtime as it would eat into his contact time as no longer living with the family. Ie he no longer sees them around the house or puts youngest to bed etc.
It's one reason why I moved away when leaving but not everyone can do this.
Leaving a child at the whims of an abusive parent is the courts normal stance. It doesn't matter to them as he can still parent. My ex husband is an excellent dad to a young child but as the child gets older with their own personality and opinions especially if female, then this is when he is no longer even a good dad. I watched this, I also watched my growing daughter slowly see him in a different way as he was changing how he spoke and treated her as she grew. At 10 (just this summer), he now considers her fair game to feel the brunt of his personality and expectations. At home, I could mitigate this but for unsupervised contact I can't.
Also he was pretty bad to me but he was not abusive all the time. He could be sweet, funny and charming. Very romantic if and when he got his own way.
But I really think you don't need to ask this question as when there is abuse in the home, it's not often constant and even local authority care can be far worse. Yes I have experienced this in my childhood.
Your experience is different to mine but I wouldn't come on here and ask why do women leave when sometimes the situation they go to, is worse than the one they left?
I only left when forced to and when I could sort out something decent for me and my kids.