We used to be on Police rota, but that all changed (down here anyway) when the AA talked their way onto the scene.
They offered to pay for the rights to TA recoveries....which the Plods accepted (of course) but the AA couldnt possibly cope with an area the size of Devon & Cornwall with their facilities.
So the rub was that if we wanted "in" on the recovery scene (which we had managed quite well for some 30 years) we would have to now pay the AA and meet all their criteria. Their criteria being;
Ability to lift a vehicle from the carriageway to the recovery vehicle
Take full control of the scene upon arrival
Clean up the carriageway
Ability to recover more than one vehicle from an incident
Ability to recover caravans/trailers
then there was the secure compound
Undercover secure compound (for forensic work to be carried out)
It became rediculous and the cost of recovery had to go up, typically from £60 to over £150 just to break even, just the cost of the equipment (without the training required) is prohibitive.
So I dont know about your area but down here the insurance companies dont have any say in who recovers anything, only the highest bidders get the work.
& that has lead to the loss of most body repair shops down here...that and the stupid prices/repair methods insurance companies want for them to be "approved repairers" ( again the highest back-door bidder wins the work)