Changing tort law would be an enormous political fight, way bigger than Obamacare or abortion or environmental regulation or gun rights or any of the other big ticket items.
Not sure if I agree with the idea, but it wouldn’t necessarily require changing tort law. Just require that the licensing body also provide liability insurance, as hospitals do for doctors; and “disbar” any police officer who uses anything other than the group-plan insurance to pay out a settlement, or who goes to court.
I believe unions already tend to kick out union members who don’t accept union-appointed lawyers and instead attempt to litigate their own cases. This wouldn’t be much of a stretch from that.