I dunno, that money can add up, and if you did pay the money, you wouldn't necessarily get a true home invasion solution. You'd just get an officer who might be able to respond to your call but would probably arrive too late. You'd actually need a bunch of officers and tactical aids and weapons for them to deal with a truly hardcore situation as well.
So on some level I think, why not just save the couple hundred dollars a year, and invest in a WASR-10 AK 47 for a few hundred bucks? Then get a few reliable magazines, and a bunch of Wolf 7.62x39 hollow point ammo. Spring for some body armor like a level IIIA vest, or level IV if you can get it, and see if you can get a PAGST helmet from the surplus store.
Setting the body armor aside, which is pretty expensive, with just the AK, mags, and ammo, you're kind of set for life with a reasonable home defense capability for the price of only 3-5 years of police protection.
I imagine that not having any responding officers for your area might help if something ever went to trial. Your lawyer could be like, "My client was more justified than most in nailing the perp to the wall with his AK because THERE ARE LITERALLY NO COPS THAT SERVE HIS AREA!!!" I think that even a soi-disant progressive would be a lot more understanding upon learning that for all intents and purposes in your area there's no police service.
I guess that as far as the costs go, I'm assuming the homeowner has prior training, and doesn't need to blow thousands on tactical rifle and CQB lessons.
And then to prevent theft of the rifle when you're not around, I guess you'd need some way to secure it in the trunk of your car or something so you can always have it with you when you're coming home, instead of needing to be home before the perp arrives in order to access it.