Lets stop there. What are we trying to solve? I'd say we are trying to solve this question: What makes a good life? STEM gets a lot of press because, obviously, it is a well paid field.
However, the answer to what makes a good life is not just money. I'd wager it is (almost) universally agreed that a good life consists of: (1) Enough money (see below), (2) a career you enjoy, (3) free time to pursue things you enjoy outside work, (4) good health ((4a) mental and (4b) physical) and (5) connections with other humans. Maybe people can quibble with this to some degree, but I think that is about as uncontroversial as anyone can be on the subject of a good life.
Accepting my definition for the sake of argument, how does a gender imbalance in STEM affect this? Does a STEM career affect all 5 of those elements? Just some? Just others? Certainly, a career in STEM provides "enough money". But is it a career EVERYONE will enjoy? Do you get a lot of free time? It seems rather unhealthy as well - there aren't a lot of healthy people in offices in general. As for connections, YMMV on that one.
I think we focus too much on money because it is so easily measured. But more money beyond about $75K in the USA doesn't appear to make people more happy: http://content.time.com/time/magazine/article/0,9171,2019628... If you make above $75K, then surely that is the time to optimise the hours of your day not towards making more money, but to add more of the other 4 elements of a good life.
STEM is not a panacea, and money is not the be all and end all of life. Trading better financial security for health, a career you enjoy and more free time and personal connections may be a sensible decision. I'm not convinced more people would enjoy STEM careers, any more than I think everyone would enjoy being a special units detective, and dealing with a lot of awfulness.