Some great answers here, but there is one point not mentioned: non-representativeness of the user sample when self-selected.
Put simply, if feedback is optional, content users do not leave feedback. Delighted users might sometimes leave feedback, if they feel altruistic. Angry users love to give feedback, to demand that somebody makes a change. The result is that you only get to know the opinion of a vocal minority, and it is hard to gauge whether the silent majority agrees with them or not. In the worst case, you may start making changes for the complainers and thus break features most users loved but did not bother to praise.
This does not mean that user feedback is bad per se, but that you must factor in this possibility before making decisions. For example, you can let the users provide an optional opinion for months or years, gather some change candidates, then make a survey (possibly paying the participating users) where the users have to commit to taking it before they have seen the questions. Once you have such a pseudo-random selection, your representativeness should be good enough for decision making based on the resulting data.