I can totally see where you're coming from. But major engineering achievements require efforts of many skilled people, who often like to be paid really well for their work. And the way the world works today is that a lot of big money is in the fields that are of questionable value to the society: advertising, finance, military, etc. And even in the fields that seem at first glance to be socially valuable, like health care, most of money comes not from healing people but from playing the game of "rip off public or private coverage providers".
Therefore I think the best we can hope for is that engineering breakthroughs achieved in profit driven fields will gradually leak into other fields where they can actually be used to improve people's lives.
This is why federal research and development agencies should pay higher salaries to attract said engineers.
Breakthroughs achieved would be funded by taxpayers and customers of these agencies and the patents for technology produced would be more likely enter the public domain.
It is very hard to get a large group of people to work efficiently towards some goal; very few organizations manage to do that. As far as I know such success stories are even more rare in the public sector than in the private sector. This means diverting resources away from private enterprise towards government agencies is not guaranteed to improve the situation.
Therefore I think the best we can hope for is that engineering breakthroughs achieved in profit driven fields will gradually leak into other fields where they can actually be used to improve people's lives.