It's hard to overstate how terrible this idea is. GDP is a concrete measure that is difficult to fake. Once you start arguing about the economic value of volunteering, divorce, income inequality, and crime -- you've opened the door to never being able to trust GDP again. Should we create new metrics to track progress? Sure. Should we stop tracking GDP? No way.
Seriously. If there was an obvious alternate metric, we'd already be using it. Measuring well-being and happiness will never be straightforward and uncontroversial, despite what the authors of the article say. You don't need to look much past the first few paragraphs of the article to see an obvious bias about income inequality. That reveals what attempts to find new metrics are really about: the authors want to use…
But to argue the point a bit more, and this is something that Thomas Piketty (an economist that studies inequality) always brings in his books: one measure is not enough. GDP is one measure, we need to look at many more measures. GDP does say something, it's not meaningless, but we need other measurements to get the full understanding of the picture.
And we actually have lots of them, GDP sadly fails to capture a lot of externalities, so it doesn't really capture very well for example environmental damage; think of china, their GDP is growing a lot but we can all see it's not growing in a sustainable manner. Or think of the USA, highest GDP in the planet but this isn't being reflected in life expectancy for example which actually has been declining for a while now.
And as I said in the beginning, inequality very much affects people's well being and the well being of an economy as a whole as well. So it is definitely a measurement that we ought to take seriously. It seems silly to me to say "these are left wing metric". These are metrics that have a reason of being, inequality has real effects on our economies and there is a lot of work, and good work at that, that you can read on why precisely this is the case.