To the original point, this could be a lot of things. First, the system could have been left "wideband" and the vehicle and portable radios programmed up in narrowband. That would automatically make them a lower volume - and all at a constant level. Are there systems that haven't narrowbanded? You bet there are. Lots of them for all kinds of reasons spanning from lack of knowledge to deliberate choice. They will sound louder on the dispatcher end and the mobiles will be significantly softer. The dispatcher won't notice because she doesn't listen to herself in the headphones, only the cars/portables. They all sound fine, and they're all at a level and volume she can adjust to hear comfortably.
The other situation could be that comparator output, or "poor man's microwave" (UHF FXO) links (if they use them) are set too low by people who probably should not be playing with radios, or the systemwide compression is not in line with the console output.
Lots of stuff spanning the continuum.
It may not be a problem for the cars because sometimes there is a compandoring scheme used in narrowbanding where the vehicle receiver expands audio beneath a threshold to a certain value and the dispatcher audio might be above the compression point. You won't find that in a scanner. So, that might be it, too.
The one thing I'm pretty sure of is that "scannerland" probably factored nil into why it sounds the way it does.
Actually there is something that can be done, but it involves spending. If you feed your audio into a professional mixing board, you can limit the gain and set compression points so that low sounds come up and high sounds go down or stay at a fixed point. It's also wires and other stuff all over the place. Probably a little extreme for casual listening - and someone might come in at a future point and set everything just right and make it work normally. Then it wouldn't be useful anymore. Alternatively, something like an MFJ 784B might help, too.