Don't even get me started on how completely and totally useless home (and even commercial) burglar alarms are. They are a complete waste of money. Home owners would be better off lighting their money on fire. At least they'd get some heat out of it. Alarm companies are selling a false sense of security in most cases. That's about it.
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I see the points you're making, but I disagree. Before I moved home to California, I was living in the North Dallas area, in a suburb that was, at the time, the safest city in Texas for its size. There was virtually NO crime in my neighborhood. We'd joke all the time that 3 or 4 squad cars had to show up for an expired tag because they didn't have anything else to do. Ha ha ha.

Until I was home one night when someone tried to break in. My husband had just left to visit a friend. My dog and I heard the sliding screen door opening, and we both jumped up and ran to the living room, and there's this guy trying to jimmy the sliding glass door open. My dog scared the shit out of him and he went running. My husband came right home. The police told us there hadn't been ANY crimes in our neighborhood recently so this had to be a freak incident. Whatever. We got Brinks a few days later.
Now, back home in CA, and in the ridiculously safe city I grew up in, we have ADT. They've come a long way from ~20 years ago! For example, in addition to the standard stuff, like glass break detectors, motion detectors, alarm-wired screens, they also have cameras. In my house, because of pets, motion detectors are out. I didn't like glass break detectors when I had them before, so they're out, too. So what we have is a combination of door alarms and wired screens. For me, it's not so much about stopping a burglary when no one's home as it is alerting me if someone breaks in WHILE we're home. I went into absolute panic mode after that attempted break-in, because it felt like, well, another violation (I don't want to go into the first violation I experienced). All I could think about was that if I had been in bed (I was recovering from minor surgery) with the bedroom door closed, my dog and I probably wouldn't have even heard the screen door sliding, so the guy would've been *IN* my house. I'd rather have an alarm go off to let me know so at least I can react.
It was the same when I'd go in to the office on weekends. I'd do that when I needed to do something involving bringing the system down, so I wouldn't disrupt the employees' work during the week. We were in an office complex, and there were usually no, or very few, other people around the complex on weekends. Even though my little boy (my 183 pound Great Dane) always went with me, I was still glad for the alarm system. Again, if someone broke in WHILE I was there--alone!--at least I'd know about it.