I doubt that it would be legal to do so, but I'm not a lawyer, so suffice it to say that it's not practical because they would be removed from their management positions very quickly.
Google actually explicitly put something like that in their IPO report ("focus on the user and all else will follow" as facebook helpfully brought up recently).
Now, Mark Zuckerberg also put similar statements in his letter to investors, and you could certainly make the case that these statements don't guarantee that the user will be put first, but investors have still been alerted that decisions they don't like may be made if they're deemed important for long term growth (google's voting shares scheme also helps in the regard).
For companies in general, though, the reality is that the judge will almost immediately throw these cases out unless there has been a major stumble (see, for instance, all the thrown out stupidity around demands for a documented and public Steve Jobs-succession plan). Even then you pretty much have to prove that the actions made were negligent without any kind of foreknowledge of how the market is going to behave. In other words, the only people that end up making money on these suits are the ones in cases where the company settles to avoid court time.
It just irks me that people often use the myth that they must maximise shareholder profits at all cost as a reason for why companies act evil. The Harvard Business Review article, that a still can't find unfortunately, also talked about how this myth is pervasive in management circles, and leads to bad business practices and corporations being socially unresponsible. I got the impression that you were insinuating this.