The scanners were put in because too many people were misssing their callsign when using the (at-the time) Spectras to scan the other agencies.
I see several flaws with this philosophy. Starting with the perception that one agency must know what the others are doing in order to function within their roll, I question how true that would be, outside a major incident operating under unified command.
Priority scan works pretty good, but it requires careful consideration of how many channels are allowed to be scanned. Receiving ones own traffic while stopped on a scanned talk group relies on the priority scan data carried on the voice channel. It's possible to set priority scan to an excessive number of talk groups. In conventional operation, it's reliant on the priority revert where the radio samples it's priority channel, making that audible tick heard while scanning. At worst, you'd miss a couple tenths of a second of transmission.
In any event, if scanning is causing problems, adjustment needs to be made somewhere, and part of what gets looked at is what actually NEEDS to be scanned. In some cases, a joint dispatch operation may be what's called for.
And finally, if one agency goes encrypted, defeating scanning, and problems arise between agencies, management and the local politicians need to step it up and formalize cooperation. That could include creation of a JPA with a regional system under common control.
At a truly professional level, encryption is not an impediment to interagency cooperation. If it is, someone somewhere is not operating at a truly professional level.