I think parking chairs are a novel and relatively neighborly solution to the issue.
Neighborly is shoveling someone else's car out. Shoveling out your own is self-serving -- nothing wrong with that. Insisting that you own some bit of public property is selfISH. Shoveling your snow onto my freshly-cleared sidewalk and then claiming the bit of road in front of my house (and this after I just shoveled his walk for him that morning) is asshattery.
If you want to use your car, you shovel it out. If you want to park it and you need a space that isn't clear, you shovel one. It's the price of owning a car, and not paying for the real-estate to house it.
On-street parking spaces are a shared resource. You leave for work, I park there when you're gone, I leave before you get home, you park there overnight, and so on. But just because you shoveled a space you want to claim it 24/7? Sorry, you need to pay for some kind of permit if you want to do that, just like I need to pay for a permit to leave my dumpster on the street.
Otherwise, anything left in the street on trash-pickup day should be hauled off to the landfill.