It might be easier to convince people to not grow lawns if we'd do away with some of the stupid laws and ordinances that require people to have "well groomed" lawns in places where such grass is an unnatural imported occurrence.
Perhaps even offer some tax breaks or other incentives to "zeroscape" or landscape their yards using native plant life suited to the climate. A yard without a lush verdant lawn need not be an ugly yard. It can still have plants and look nice without grass, if we'd "normalize" more nature/planet friendly practices instead of punishing people for not being destructive to their environment.
I bring this point up because here in Utah many neighborhoods will actually fine you if you don't have a lush green lawn in your yard. (Unless of course you're rich, then somehow you magically get approval to go the zeroscape route if you so desire.)
I would definitely like to see it taken farther as you have suggested -- give tax breaks and subsidies for people xeriscaping or replacing lawns with synthetic turf.
And it definitely works. I knew a lot of people in HOAs that mandated residents eliminate a certain amount of lawn due to these fines.