Sounds nice. But GDP is used by the government, to help set policy in many ways. It's relevant to what I think should be part of the business of government: Keeping the country's economy running.
The clamor for the government to track happiness instead of mere economic indicators implies that happiness, too, is now the government's business. And I find that creepy. Keep the government focused on economics. We should not give it the authority to look after our happiness.