My spin is that the bad guys who are serious about their trade, the big time traffickers and the like, the ones who will spend $25,000 to rig a mule vehicle with traps will easily be able to purchase and install the technology to track our vehicles. Imagine how good it could be for your business if you knew where the cops were all the time. Imagine how easy it would be for a terrorist cell, who are technologically adept and VERY well funded, to take out every patrol in 5 minutes time because they know where they all are. Go ahead, call it farfetched, but there are people who would have said that about not 1, not 2, but 3 (and almost 4) commercial airliners being used as kamikaze flights against us.
If your cruiser is emitting a signal which constantly gives your location and that signal can be received by your HQ, then the signal can be received by the bad guys. Encryption is nice but you get a motivated 13 year old and the best encryption can fail. The expense of maintaining such a secure network would be prohibitive IMO. One cloned hard drive from an unscrupulous civilian contractor with big debts or an expensive nose candy habit and (zip!) there goes your security.
Officer safety is a valid argument; in that case if you hit the panic button on your radio it should transmit your location. If HQ is unable to reach you, they should be able to trigger a location hit. During a pursuit or other specific circumstances, you should be able to transmit your location so a supervisor can coordinate the operation. Control of the transmission should lie at the officer's discretion (bona fide emergency situations notwithstanding). If management thinks you are sleeping / shirking / speeding / slacking, let them provide just cause before sinking a boatload of money into a Big Brother system. Nothing like the feeling that it's OK for you to carry a gun and deprive people of their freedom of movement and liberty, seize copious amounts of cash or narcotics, but you can't be trusted to drive a car. If your administration wants to know where you are all the time, they should hire a supervisor to ride along with every patrol.
Also, if it's such a good idea, answer me this: Do the patrols themselves have the capability to bring up the map on their computers and see where their backup is, or are only supervisors granted this privilege? Hmmm...