Sure you can pay for air today, but it's always for non-standard purposes. SCUBA, industrial, CO2 cartridges for flats, etc.
We've already gone down this road with respect to water. The cost of manufacturing bottled water far exceeds the cost of having clean water on tap. Corporations (Bechtel) have even tried to make rainwater collection off of roofs illegal.
My point being that if you are going to define property, you should make an effort to define between (what should be) non-divisible communal property and private property.