Publicly held companies have a fiduciary obligation to maximize shareholder profits. This can lead to all sorts of pathological activity.
Non-profit companies are prohibited from rendering an investment profit. This leads to some classes of inefficiency and drives away a lot of people who might otherwise like to participate.
I think we need a designation in between, a company that is bound to follow a well defined mission of some kind, but also wouldn't mind making some money at the same time. Not obliged to be evil, not beholden to shareholders, but not divorced from the market.
By the way, Google sees itself this way, if you believe their mission statement and their founders, and I do. Over the years I expect that Google will come to see itself as just another profit driven machine, but I think that as of now it still has some idealism left.
Craigslist is another place that seems to be operating this way, and I think their idealism may survive even longer.
It's the company everyone wants, but there's no place for it in the regulatory or investment schema. Maybe there should be?