Yes they all should be absolutely 100% abolished.
I'm sure you would agree that there are cases, however rare, of parents abusing their children. What system would you put in place to protect these children? Should the Church be responsible for them?
To be clear, by abuse, I mean true abuse; like a father raping his daughter or a mother neglecting her baby to the point of starvation. Again, rare situations, but they to occur, regrettably.
The state can act to protect citizens from crimes, that is very different than what we have today, where false allegations = guilty and no due process. The foundations of the British justice system is based on Christians values and some of that remains but we are in a godless state too.
As far as child abuse and kids who end up with either wack jobs or cruel parents, I think the best "defense" is a society where people live according to natural law. There will typically be very large families, multigenerations, people will be in check, there is somewhat of a buffer there, there would be extended family to live with, you wouldn't have 13 year old girls selling themselves for crack to get away from the mom's house with the mom's boyfriends who rape her or the boys just totally abandoned. Grandma or the sister of the mom starving the baby would see something was wrong or it would not get to that point in the first place.
Even with my own husband, I think if we had remained living close by people of his nationality who happened to be very good people, things would not have escalated how they did. Even if he cared less about me and our children, he would have had to face them. OTOH I saw how being around people with anti-Christian values influenced him in not a good way.