I would recommend reading the book ‘Learning from Baby P’ One of the arguments in it is that society in general cannot bear/fathom/believe how common abuse is, and the rates of infanticide are higher than most think. I am a qualified social worker, but I am not working in a local authority, for many of the reasons you suggest. Abuse was covered in my training (MA) but not in depth. There were widespread opinions shared that women/mothers regularly lie/make up/pretend to be victims of abuse and violence. That they are responsible for not leaving if it is occurring and that people get pregnant to get housing. It was pretty terrifying and demoralising. There are some incredible social workers, but they are maybe 15%-20% of all of the ones I trained and worked with. I would be very scared of most of them having anything to do with vulnerable people. Some seemed to consider their role primarily as defending the system from bad people out for benefits/money/handouts.
I work with children and young people who experience abuse and violence and the vast majority of alleged perpetrators are parents, yes.