Well, I do have a take home (fully marked) cruiser and I'll tell what I think. It has its ups and downs; first off it is nice to commute in the company car and not pay for gas or tolls. I commute quite a distance, so this is luxury. You can get everything set the way you want without anyone messing it up, and even go to court on your time off in the cruiser. But one also feels obligated to stop for DMV's and occassionally I even have to stop for accidents. I DON'T get paid for this time; this is on my own dime. I do log the incidents, so to give SPAM more ammo when the senate wants to take our cruisers. Every year SPAM has to fight some intiative to "save money" by taking away our take home cruisers. Also, we can (and I have been) called off duty to respond to emergency incidents (riots, protests, etc.) and going in the cruiser decreases the response time. (one of the reasons the state police is such a paramilitary organization is so we can assemble quickly, with overwhelming force and a clear chain of command quickly).
Take home cars certainly decrease the maintainence needed on cars and people being people, you tend to take better care of a car you essentially "own". Many troopers spend considerable sums to upgrade and customize their cars, something unknown to most locals. And, of course there is the detail situation, it is certainly nice to have a cruiser to drive to details.
Unfortunately, your cruiser also brings unwanted attention off duty. Yes, your neighbors are certainly going to be aware of your occupation, but so will any fool who drives down your street. I've heard of troopers having their doorbells rung, and finding some clown who is lost asking them for directions :evil: . Additionally those of us who live in the cities have to be worried that some little turd will toss a cinderblock through your windshield. (God help him if we catch him!). Overall, though I think the benefits outweigh the negatives. Visibility in your neighborhood probably deters crime rather than increasing it. I believe that most departments would benefit from having take-home cars.