I'm undecided. On one hand, we do elect the Mayor who appoints its members, so the people do have an indirect say in how they would like the Board to be constituted. And democratic unaccountability is theoretically useful in pursuing the greater good over parochial interests (see, e.g., the New Deal justification for the federal administrative apparatchik).
On the other hand, the Zoning Board makes decisions on issues that have a tremendous impact on the quality of life of Stamford residents--in many cases more impactful than decisions of the Board of Finance or Education. Just this week, the Zoning Board has approved the demolition of the giant cylindrical tower across from the government center, to be replaced by luxury apartments. It is also considering allowing a Chick-Fil-A at the intersection of Long Ridge Road and High Ridge Road where Bank of America used to be, and a Life Time Fitness in the office park to replace the old Frontier Communications headquarters. So the counter-argument is that the officials who make these decisions should be answerable to the people to the people who are affected by them.
What do you think?