Back when I used to be an ambulance paramedic, it was pretty typical for the police to get to a scene first, followed by a tie between our ambulance and the fire department. That's suburban living for you. We all responded to many a scene together, to make sure there was adequate manpower to handle whatever was going on.
One night, I was training some new people. A driver and what we called "a third" - the third person on the ambulance that did whatever, usually the least senior of the bunch. Anyway, I'm sitting in the passenger seat and we pull up in front of the house we were called to. No police in sight, no fire department yet. We beat them all. But the house was pitch dark. Not a light on in the place. And as we pulled up to the curb, I saw one of the front curtains moving. I instructed the driver to get us out of there, and quickly. I radioed the police telling them what I saw. They were only about 30 seconds behind us it turned out. We watched them surround the house from our safe parking place down the block. They radioed back in not too long canceling us. No medical emergency. I don't know what the deal was with that 911 call for an ambulance. The curtain could have been moved by a cat for all I know. But I wasn't about to be the first one into the house to figure it out. Not many people call an ambulance with no lights on in the house. It does happen, but an experienced paramedic will approach that situation with caution and suspicion. It was a busy night and we went on to other calls, as did the police. I forgot to follow up with them later to see what the deal was.
Bottom line: You can't help anybody if you end up injured or dead. So as a responder, your safety has to come first. The police will go into situations that I wouldn't. They are better trained and equipped for that. But they will be on alert and watching out for their own safety as they come to assist you. If you suddenly hop out into a hallway with a gun in your hand - even if you're the good guy - they aren't going to know that initially and you are putting yourself in potential danger from their response. I have thought about this a lot over the years, and that is why I'm not inclined to want the police entering my house, armed and full of adrenaline, in the middle of an uncontrolled situation. If I have been able to implement my protection as pre-planned, and I am in one of my "barricade rooms" behind concealment/cover with a loaded shotgun pointing at the only door into the room (ideally with the door being closed), then I might consider calling the police even though the situation is not totally controlled. I would give the dispatcher I'm talking to on the phone details of where the room I was barricaded in is located, and tell them NOT to allow their officers to attempt to open the door prior to negotiating the exact process to safely do that with me on-scene. Probably would involve the officers on scene cranking up their radio volume, holding the radio up against the door, and let me talk to the dispatcher over my phone and hear the dispatchers response come back over the radio. "Two factor authentication" as it were.