"Law enforcement policy would never permit firing into a building occupied by uninvolved, innocent people. That's why it was necessary to locate his room and breach it from the hallway."

Totally agree.

That's also why, even after identifying the room, they didn't just open fire through the door. There was no way of knowing who was on the other side of that door. Just the shooter? Shooter and hostages?

This whole crazy idea kind of reminds me of Uncle Joe's suggestion that, if we want to keep intruders away from our homes, we should just "fire a shotgun through the door".