I suspect one of the bigger problems with the plowed-in, untouched car is that tow trucks cannot easily tow it. Not only can't they find an attachment point for the tow, but if you simply drag a car out and over the massive iced in area it's stuck in, the car is likely to be damaged. And you can't ticket it because not only can you not see the license plate nor the window to put it on, but the ticket would get lost/soaked beyond recognition before the owner gets it. If a tow truck succeeds in towing, the space will likely still be unusable until someone else shovelled it out.

I would doubt anyone (except owner of unplowed car) would object to a massive extra fee to get the dang thing towed out and super extra fees for daily storage. Bingo for Pat's Tow, and a bonus for the city too.