To be honest it's a bit of a stretch having your own vehicle delivered to you after insurance. If you can't care for your own vehicle why should someone else. If your vehicle gets impounded it's part and parcel to go and collect it. Having the ability to have your vehicles moved around at the press of a button simply by paying 4x the amount is easily abusable and in no way shape or form realistic. You would have to give your keys to said person retrieving your vehicle, have them go and get it and then return to wherever you wanted it. This alone would take a long amount of time in which it would actually be faster for you to retrieve yourself.
The only way I could see something like this working, is an actual RP element to it. Having someone set up a dedicated twitter account for this could make sense but the issue of accessing someone elses impound list and key transfers becomes apparent. Coding all of this would be an absolute nightmare and would cause untold amounts of issues with people gaining access to others lists improperly.
All in all I think retrieving vehicles from impound is an extremely small price to pay, if anything it's a blessing given you can leave your vehicle anywhere in the city and know exactly where it will be after a storm. If anything I think it should be more punishing for people. When the economy was upside down due to the store changes people were driving extremely carefully as no-one wanted to pay 2-3k for a repairkit. Now everythings back to normal no-one seems to care if their vehicle flips several times as all they have to do is get out and wait 60 seconds and it's brand new again.