That seems extremely difficult to prove.
1. There's a case to be made for anonymous reports which the current system allows and your system wouldn't allow. Abusive parents can also be violent parents, it's understandable that in some cases teachers or people who know about the abuse going on wouldn't want to report that abuse.
2. This also reverses the current issue with CPS where a report leads to an investigation that's traumatising for the family and the children that CPS is supposed to protect. If you investigate any report to prove that the report was made in bad faith, then anyone reporting will potentially have to go through a process that's traumatising even if they are not guilty.
I think instead snozolli's solution of making CPS' investigations less threatening and more humane with an expedited process when there was clearly a misunderstanding and creating laws that make it clear that certain behaviors are not negligence would go a long way toward solving all this.
But in instances where someone has incontrovertibly made a false report because they wanted to ruin someone's day (or life), that should follow them around. There is a large blurry area between reporting someone because their kid has a black eye every couple months and reporting someone because their kid is better at baseball than yours where you can't prove bad faith, and in that instance it doesn't make sense to ruin anyone's life.