I could see a situation whereby a NPC auths the towing truck driver/service member to go collect a specific wreck off the street as maybe a once a week activity?
I.E. A wreck spawns -somewhere-, most likely in Red, takes from a few hours (in say green) to a few days (in red) until the orders come down to remove it, and then the player is able to tow it back in to the service area. If they can scan it and determine that it's a player owned vehicle, they can impound it until the owner pays to get the wreck released to another garage or repaired, and if it's a NPC wreck, they might say something along the lines of 'This isn't salvageable, take it down to the crusher and get it recycled.'
Spawn one or two wrecks a week on an automated manner so that tow truck drivers have intermittent work to do if there's not much vehicle combat going on (or until it's fully implemented) and then use the flagging system on all wrecks on public streets from there, including system-generated wrecks, as well as wrecks generated as a result of vehicular combat.