Ann Lipton posts an interesting discussion that I would summarizes as follows: Benefit corporations lack means to make credible commitments that they will in fact remain committed to their beneficial purpose even if, for example, a rapacious hedge fund obtained control and tried to maximize shareholder wealth. In an sense, of course, this is just a variation of agency cost economics.
Probably the only mechanism that works over time appears to be vesting voting control in the hands of ideologically committed insiders. Consider, for example, Prof. Lipton's discussion of Lemonade and Vital Farms.
But that, of course, presents an entirely different set agency costs; namely, the set of costs associated with having a controller.
So here's a research project. (Just thank me in the asterisk footnote.) Design a monitoring mechanism with effective sanctions to detect and punish defections. And/or design a mechanism by which the benefit corporation could give hostages or otherwise offer a bond that makes their commitment more credible.