Public safety digital radio networks are primarily APCO Project 25 (P25) which use IMBE/AMBE developed by DVSI. Motorola's original digital radios used a proprietary vocoder called VSELP (also used by iDEN/Nextel). When APCO standardized public safety digital radios, they rejected VSELP and chose IMBE from DVSI instead. Personally I think VSELP sounds better than IMBE, and I'm not sure IMBE was chosen due to technical superiority or if it was political reasons (i.e. picking a non-Motorola solution due to Motorola's dominance). Also, APCO Project 25 Phase 1 was not TDMA, however Phase 2 is.

https://en.wikipedia.org/wiki/Project_25

Public safety radio is a true mission critical service that moves slowly - equipment lasts years or decades and is expensive and not frequently replaced or upgraded, hence new technology adoption is slow. Vocoder choice is driven by a standards committee for interoperability (which has seen more emphasis since 9/11), and of course committees aren't typically known for working fast. Public safety radio is definitely not a place for a "move fast and break things" mentality.