From what I understand, it's a bit of the opposite. That is, shareholders don't have that much influence over things like executive compensation, which seems to be a bigger culprit in terms of American wealth inequality than outsourcing. Plus, as MCG put it, lower labor costs do lead to cheaper consumer goods, which the middle class is rather fond of.
Honestly, I'm not that worried about jobs moving across borders in a general sense. Every major developmental success story has involved access to the US and/or European markets, and first world countries have had very healthy booms even in the neoliberal trade era. The arguments against outsourcing (American citizens need to be protected from foreign labor by being given a monopoly) are basically the same ones made against immigration, which should slow you down a bit if you're a liberal.
It really does suck when a real large segment of an industry leaves, though, because you've got people whose career and work experience suddenly mean very little, through no fault of their own. We'd probably do better to focus on those cases rather than get angry about any job going to any other country at any time.
