Avoiding overflight of local communities could result in a longer route, with aircraft burning more fuel and producing more emissions.
You can liken this to a road bypass of a town. Roads that go directly through the town centre are sometimes replaced with a bypass (avoiding the need to drive through the town) however this often results in a longer journey around the town. The congestion and negative effects on the town are reduced but the amount of fuel used and the emissions produced may increase.
When designing airspace, we could:
A. Design flight paths that prioritise the reduction of aircraft noise for local communities over those that reduce fuel burn and emissions; or,
B. Design flight paths that prioritise a reduction in fuel burn and emissions over those that reduce noise for local communities.