The whole problem is finding out exactly where the property line is. There is a whole army of professionals that do that, full time -- surveyors. And there are databases of lots and zones that local governments maintain (some even behind pay walls). So finding out where exactly "private" stops and "public" begins is not that simple.

The issue might not be that big in areas where nobody cares about land that much, but in NY, LA, or other big city, where the cost of land is so high, every inch counts.

So you paint the curb red and install a fake fire hydrant. Is the curb yours or not? I don't know. Can you "impersonate" a fire hydrant to stop others from parking in front of your house? Not sure. It seems like it would be illegal. Kind of like putting a fake "highway entrance" green sign on the side of your house. It is your property but if it start directing traffic into your neighbor's pool you might just get fined or sued. At least a law will quickly be created to deal with the issue.

Point taken, the city usually owns the curb, I think... but has a painted curb been defaced, or merely weatherproofed in a colorful, free-expression sort of way? On the other hand, stop signs and the like tend to be stuck into private property.

There's definitely some funny business when it comes to signs and sidewalks; e.g., the landowner owns the sidewalk, but is required to keep it clear and level, not prohibit the public walking on it, not turn it into a flowerbed, etc.