It's easy to dump on green committees. Most of the time they deserve it, and I've written my share of the criticism. But one thing that's overlooked for the most part here - though Bill McBride, above, comes close to it - is that a green committee/green chairman must be an advocate for the superintendent, not only in terms of salary and overall budget but also in the form of capital improvement and management practices - equipment, timing of aerification and topdressing, tree management, that new irrigation system, and all of those other invasive practices that produce certain turf conditions, such as "firm and fast."
So yes, the green committee must work closely behind the scenes to establish what the club wants and to communicate this to the superintendent, but also to communicate back to the club what the superintendent needs for the best interests of the golf course - which, if the green committee is really doing its job, is more importrant than what any golfer(s) want. That means communication, golfer education and club politics. That's the green committee's real job, not micro-managing agronomy or the depth and color of buinker sand.
The real benefit that a green committee provides is as the advocate of a maintenance schedule that doesn't succumb to the golf calandar (i.e. "we need to aerify the first week of September, but it interferes with our Challenge Cup, so let's put it off three weeks").