I think America would be much safer if the bad guys knew that their peers routinely met their demise during the commission of a crime due to an armed citizen.
Brady folks are talking about a pretty much disarmed society in many high crime areas.
How many states have constitutional carry or shall issue? We don't routinely hear about two permit holders getting into a gunfight over some perceived threat, normal circumstance is generally clear cut that someone was committing an offense that warranted the citizen's use of force.
Constitutional carry, though, cuts both ways, we've seen recent events where the bad guy was not a prohibited person, so the Brady true believers will conflate their actions with constitutional carry where possible.