It is done, but doesn't work well at all. The sections of the outside of the building that go across your unit is your property (including the sections of the roof, siding, etc). You mow the grass in front/behind your property.
As far a street maintenance, that is the big concern, as no one pays to have it done, and if the city doesn't own it, your are SOL. The only one I know of in Columbus is Dublin Commons, but there are likely a couple others as well.