@AviK
I can only speak to CT where I know who the administrators of the Bar Examining Committee are.
Yes, many of them are attorneys, but they have been bureaucrats working full time for the government for their entire careers, also the chief judge of the Superior Court (judges are not elected in CT).
They tend NOT to be members of the Bar Association which is composed mainly of attorneys in public practice.
Membership in the Bar Association is not a requirement to practice law in CT and I know many attorneys who do not spend the money to belong.
The Bar Association in CT has far less influence than it had 30 years ago.
CT currently uses questions from the national testing service for its state exam day, it no longer constructs its own exam, so Bar Association influence has no bearing on the test at this point.