If you created local dump sites where trash could be sorted and composted, it could work. You also cut down on the amount (and as a result the energy) of trash that gets thrown in the dump. Obvious obstacles are the inability to get people to use the local sites, the initial costs / availability of land, and the resistance to dumps in neighborhoods.
A potential 2nd level effect would be the long term state of trash dumps. At least some dumps are eventually reclaimed. Would reducing or eliminating the organic content prevent that from happening?