This is not true. Planes fly for many reasons. Load Factor is just one of them. Maintaining slots at airports is another. Moving cargo is a third. Staging aircraft for other, more profitable routes as well.

I know it's counter intuitive, but once a route is established, flying on it reduces the co2 per passenger.

Don't take it from me, take it from the carbon offset people:

http://www.co2offsetresearch.org/aviation/Occupancy.html

Nope. You are simply ignoring the role of passenger demand in creating more flights. Additionally, CO2 per passenger is not the only consideration for sustainability; the goal is minimizing total CO2 output, i.e. total number of passengers.