The government certainly has not done much to help support improved margins and value for natural gas producers but the localization of natural gas (inability to export) and overall influx of new drilling and discoveries is the main reason for depressed prices.
I agree the cut back in production could impact natural gas prices but from my research the main reason they are shutting in fields is economics and the reduced margins or negative cash flow so they would rather wait for an improvement in prices to open production back up.
"My well came in big, so big, Bick and there's more down there and there's bigger wells. I'm rich, Bick. I'm a rich 'un. I'm a rich boy." - Jett Rink
Don't believe anything I say. Do your own DD. Insert huge disclaimer here ____________.