The LAPD had the greatest system ever in the original "ROVER" system.
The Rover System was put into operation just prior to thre 1984 Olympics and worked flawlessly. Having worked on parts of Rover, I can say that it was by far the best system I have ever seen to this day.
It more that proved itself during thr Northridge Quake.
Looks like they kept the major part of the original system and added the P-25 to it. Good for them they are smarter than most.
As far as getting permission not to go with a trunked system, I don't know.
I will say this, they probably made the right decision since I would not want to base my safety or the safety of others on a Trunked System, that seems not work as advertised. Too many failures possible.
Maybe the City of Los Angeles was not dazzled by the sales pitch of some salesman.