Mark C,
I generally feel as you do about committees as they tend to reflect the quality of the people who are drawn to such things (IMO, too often theorists vs. doers, well-meaning generalists who don't accept the limitations of their lightly acquired knowledge). Yet, a small group of experienced golfers, say 3-5, with time to devote to understanding the objectives of the club and the ability to check their egos at the door can serve a useful purpose as Sean and JM noted.
Though not necessarily or directly in the purview of the green committee, I am aware of a very upscale member-owned Texas golf club which discovered in the past year or so $millions missing from its accounts (the miscreant, lacking funds to make payroll, finally called a board meeting to surface the problem). Coming from a finance and accounting background, how the books were cooked for a few years without someone noticing is beyond my comprehension. It is a club which used a corporate management structure and its members were probably too busy to essentially manage its own management company. Hopefully its books were audited by a well-insured CPA firm and the members have some recourse.
A good green committee can serve to protect the deserving superintendent from the whims of the membership and the membership from an under-performing or crooked superintendent (e.g. if weeds or animal damage are rampant, yet the records show receipt and application of chemicals, a vigilant member may contact his counterparts at other area clubs to see if they're experiencing similar problems, and if not, start looking at the records themselves).
The committee can also serve to help modify plans and budgets to better address changes in conditions- e.g. if armadillos are going crazy after an ineffectual chemical application, instead of spending the budget for blowing clippings x/week, adjust to x-1 or 2 and maybe hire a pest control firm to handle the problem. Take some of the heat of an overburdened superintendent; give support to some of the necessary decisions that at times have to be made on the fly.