Both 2nd amendment activists and anti-gun people make the same mistake here: the physical presence of a gun changes everything. Guns favor the offense, not the defense.
The solution is always the same: if the opponent has a weapon, you bring bigger weapons to subjugate them. APCs will allow you to move forward without risk of getting shot at, while heavy weapons like grenades and rocket-launchers destroy the cover and concealment of the defender.
The first step is recognizing the root of the problem. The handgun. Remove the gun, and the heavy-weapons wouldn't have been necessary. But as long as the general citizenry has access to firearms, it is necessary to give bigger and better weapons to law enforcement.
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Consider this: how would YOU form a perimeter around the house safely and effectively? An APC is the natural weapon: thick plate to provide immunity to small-weapons like handguns. If the local police only has one APC however, that's not enough to form an effective perimeter: you can only cover one side of the house.
So you put men around the house, and hope that they don't get shot. And those men remain at risk throughout the duration of the siege. Thick body-armor doesn't protect the head, and it still gets hurt to get shot at.