That would antagonize the wizengamot very, very badly. Not a good long term strategy, even if you intend to dissolve it. Destroying it, explaining, and letting them work through the logical implications on their own suffices. If most people lose the ability to halt dementors at all, and a few people gain the ability to destroy them outright, they are no longer usable tools of enforcement, and disposing of them all together becomes quite urgent.
That would antagonize the wizengamot very, very badly. Not a good long term strategy, even if you intend to dissolve it. Destroying it, explaining, and letting them work through the logical implications on their own suffices. If most people lose the ability to halt dementors at all, and a few people gain the ability to destroy them outright, they are no longer usable tools of enforcement, and disposing of them all together becomes quite urgent.