You wouldn't last long in Chicago with that sort of attitude 
You've clearly never experienced a really heavy snowfall in bitterly cold winter weather in a densely populated urban area that only closes for business when snow is waist deep, and people are expected to show up to work on time regardless of the weather.
Yes, the streets are public property, but the shoveling is your work and not the effort of the interloper. Others are welcome to keep a snow shovel in their boots in winter and dig out a spot for themselves if they want to park. But we're talking about people who wake in the morning, and in order to get their car out and driving, shoveling is needed. Nobody else was equally willing to clear it because nobody else was snowed in there but the person who was obliged to do the heavy work of digging it out. And they couldn't have driven into it, snow and all...
Taking advantage of someone else's hard work is not ok, and it doesn't matter how much you 'feel' you want or even need to park in a shoveled spot. Once someone else has shoveled it, you are obliged to keep driving and find your own spot. It is part of the social contract, an unwritten law of life in the city.
It's not the equivalent of the allotment thief because she stole the use of privately rented property that was under someone else's name, and it's not the equivalent of laying permanent claim to a park bench because everyone knows Dibs is a temporary matter. Nobody would leave a Nativity scene out to claim a spot when there isn't a considerable snowfall or when they were expecting guests, or simply because they believed the spot outside their house was somehow theirs forever.
People park their cars on the streets outside their houses or apartments because there isn't anywhere else to park. It then snows, and where the shoveling and Dibs situation arises, we're talking about a lot of snow - 6 inches, a foot, etc. In the case of a very heavy snowfall, the city ploughs will also cast a two feet high berm of compacted snow/ ice that you have to hack through too, in order to get your car out of its spot.
Cars get covered in a substantial amount of snow, and so do the streets. In order to drive your car to work you have to first clear the snow off it and then shovel all that snow off the street beside your car where it fell, as well as the original street snow so your tyres can gain traction. The snow ends up in mounds on the grass, along with snow that you have first shoveled off the sidewalk. Then, after half an hour or more of clearing, shoveling, and dumping in the dark and the cold, you can get behind the wheel and take your life in your hands all the way to work.
People take shoveling seriously because it is a huge pita and considered a civic duty as well as a matter of personal convenience. They shovel sidewalks and dig out cars for old and infirm neighbours too, because compacted snow turns sidewalks to ice rinks, and it is often beyond the power of older residents to dig out a car.
If you come home after your day at work (a day that started considerably earlier than most other days because you had to factor in shoveling time) and find someone else has taken advantage of all your work, so you have to drive around in the snow to try to find another spot and dig it out, yes, you have a right to be pissed off about it.
Hence Dibs. It's not a perpetual claim to the spot. It is a notification to opportunists that basic decency is expected, and above all that the work of shoveling is to be respected. It prevents needless fisticuffs and worse.