Well there are two kinds of public shareholders, right. There may be a small number who own large enough shares to bother attending board meetings and voting, and then there are the millions with pensions, 401ks, index funds, etc. I think you're talking about the latter, who have the same issue but a slightly different version of it. In their case, the "ill-informed management" comes down to "price goes up, buy, price goes down, sell". Through share price they wield an extremely blunt version of the same weapon.
This is almost worse, because it very explicitly cares only about the short-term price. It's also a much harder problem to solve, because you can't just tell those people "think long-term and ethically when you're exercising your impact on the marketplace!". No matter how ethical they may be as individuals, most of them probably don't even know which companies they have stakes in, much less whether those companies are heading in the right direction!
This is almost worse, because it very explicitly cares only about the short-term price. It's also a much harder problem to solve, because you can't just tell those people "think long-term and ethically when you're exercising your impact on the marketplace!". No matter how ethical they may be as individuals, most of them probably don't even know which companies they have stakes in, much less whether those companies are heading in the right direction!