I'm assuming this would reduce the amount of radio traffic for a department who would introduce such a system. Is it safe to say that?
Yes, the status buttons have been used for several decades and work on the same principal as tone coded squelch. In many departments if a unit changed their status via a button on the mobile radio, Dispatch would verbally acknowledge by saying the unit number. The Dispatcher could also send an audible tone to the mobile acknowledging the message. Information can be exchanged between Dispatch and mobile with no voice traffic. In the county where I live if there is a message for an Officer to call someone a message is sent to the officers MDT computer. Some Offers acknowledge via radio others via MDT. The Text feature via APX radio gives the same ability if an officer is on bike, foot patrol or out of the vehicle.
Americain Medical Response has started using an app for smart phones through cellular for all their dispatching in southern Indiana. There are still radios in the ambulance but all dispatching traffic is handled through the phone app. When a run is dispatched the address is displayed on the phones mapping program with a route and any patient info. The Medic responds via phone and the two way mobile radio is used only as a backup to the smart phone.
Even small LE agencies are using mobile data terminals for dispatching and report writing. Illinois was giving grants to small agencies for MDT/IWIN so crash reports could be submitted to IDOT electronically thereby by eliminating paper crash reports. Electronic reporting is cheaper to manage than paper crash reports. Same for electronically submitted traffic citations.