Actually, many police departments do this with ease and organization and its not as complex as one may think.
In one jurisdiction in general and as an example, the officer will ask "10-86", to which the dispatcher announces that they are 10-86 (which more or less means the repeater is off) and then the officer can communicate with the dispatcher. Turning the repeater off is not meant to for cars to communicate with one another, it is meant for a car to speak to the dispatch center. The argument of 2 units gabbing on the input frequency is moot.
Beauty is, that the repeater, big antenna, and tower are all connected to the dispatch console, and as such, the input of the repeater is actually monitored at the console at all times during normal traffic! The 10-86 just makes it that the transmission stops at the console, and does not continue out to the repeater output frequency. As far as safety goes, the dispatcher can still hear the other units (should they have an emergency) without any problem. Likewise, when the police officers use talk-around, the dispatcher does not hear it.
In many law enforcement dispatch centers, the dispatch center more or less is the repeater. The console listens on the input and transmits on the output; it doesn't necessarily use the repeater at all!
Turning the repeater off alleviates a lot of scannerland hearing things because, as someone stated already, most only listen to the output. Not foolproof, but works pretty good. There is nothing wrong with this practice.