The reality is that the government and the economy are so thoroughly integrated it is impossible to separate the two.
Source: truth-out.org
GDP is telling us the value of goods and services the economy produced. It is not telling us whether the pollution that results is killing us, whether it all went to produce weapons and prisons, or whether Bill Gates and his kids pocket it all. We need other measures to evaluate such things, and we have them, but they are not GDP.