Oomis, in many OOT cities, the rule you propose is actually the rule. It works well, since this way people actually shovel out the spots instead of just moving enough snow around to get their car out.
However, the reason that isn’t the rule in NY, is that there are not actually enough spots on the street for everyone to be parked there at the same time. So if your rule were the rule, the people who were at work, or wherever, when the snow fell, would not be allowed to come home for your two days. (And it isn’t as if they could park on the next block–there’s someone taking every spot there also.)
So while I sympathize with your digging out your car only to have someone else grab the spot, I also sympathize with the dude who went to Lakewood for shabbos and now has zero spots to park in in NY (under your rule).
Snow in NY really stinks. Well, actually, NY really stinks.