The failure of this metric as measure of happiness is very obvious. I can be rich person (relatively rich not that rich) and are spending a lot of money on my health problems who are making my life hell. With such metric this indicates that I'm living my best days.
It can apply across a whole economy though. You could argue half of the population is obese thanks to economic policies that improve GDP. That will impact gross national happiness.
But you can’t argue that a one off really sad rich person has meaning. Nor can you argue that that’s a common occurrence that wouldn’t immediately be lost in the noise.
I’m also unconvinced that obesity is caused by “the economic policies that improve GDP”.