I came to a similar conclusion myself and eventually cancelled my monitoring service. The police probably came quickly in this case because he actually called himself and said, "Hey, my door is busted down!" On the other hand, if the dispatcher gets a call from XYZ Home Security to report an alarm, that's a lower priority call.

The thing that I didn't understand for a long time was why my alarm company wanted my neighbor's number. Apparently, "false signals" (i.e. the monitoring service has indication of an alarm but your alarm is not even triggered) is a big problem, too. So, at least if your service can confirm with you or your neighbor that your alarm is indeed going off, that might bump up the priority of your call with the local police dispatcher. At least that's what I've read online somewhere.