The Texas abortion vigilante law owed its unusual construction to the state’s desire to immunize it from federal court review. After Dobbs, there will be no constitutional right to abortion, and thus no apparent need for vigilantes. Will the law, and others inspired by it, disappear?
Not immediately, because state governments will have difficulty, as a practical (not a legal) matter, enforcing the new restrictions, due to a lack of resources. Highly motivated vigilantes can fill in the gap.
The problem, from a red state perspective, is that the blue states can retaliate by adopting their own vigilante laws on issues such as gun control. California has already shown some interest in doing this. Look for this fairly appalling way to push the legal envelope to vanish once the blue states get into the act.