Huh. I know three police dogs and all of them live in homes with children, go to public events such as fundraisers and festivals, and are generally good canine citizens outside of work. I also live in a VERY low crime area, though, and I doubt these dogs ever actually witness any crime.
When I was in the French Ring & PP club, we often did PR Days and demos and essentially had two sets of dogs. There were some very serious dogs in the club, as well as the very social dogs. We would have them all out for demos, but then when it came time to meet the dogs, we would put away the ones that weren't particularly social and bring out the other set. Grant was always fabulous for such things. He's a sporty equipment focused dog that is worthless for PP. We'd let him bite the sleeve a few times for show then let the kids hang on him. There were a couple of typical breeds in the club that could do this as well. They were all lovely dogs (obviously as I continue to feed one of them), but not the dogs that I'd probably want backing me up in a dangerous situations.
The police dogs around here are as you describe, quite friendly and not getting much action outside a bit of drug detection and perhaps barking at some drunks. One local PD has an 11-year-old GSD as the town's police dog. Dogs that get worked a lot break down physically from impacts and get pretty arthritic. The fact that the dog is 11 (GSD even!) and still working tells me that he probably hasn't seen a lot of situations.
Another thing to consider is what level of protection do you really need? I was single and used to live in a very dangerous place, and that is when I got Harry and started training in PP. Now I'm married and live in a place only slightly more dangerous than Mayberry. I'm not particularly worried about armed home invasions anymore, and Harry is a bit of overkill for what we really need now. The next dog will likely not be a PP trained Malinois. A medium large dog that is willing to bark at a potential threat is probably good.
For the record, I grew up with a Rottweiler. My wild teen self paraded all sorts of odd friends in and out of the house and he was fine with it.
And just because you're getting a guardian breed does not mean the dog will protect you. When the poop hits the fan, it's not unheard of for even PP trained guardian breed dogs to run and hide in another room while their master is murdered. Nicole Simpson anyone?
It just proves that the dog knew OJ... I mean the attacker