An interesting proposal to establish a volunteers' working group but the problem I see with it is finding volunteers who would be willing to do the "mundane tasks" as you put it.
I don't really understand the cleaner analogy. Cleaners don't have the responsibility of keeping an organisation running.
A more appropriate analogy might be one of councillors on a city/town council.
As I understand it, there is currently no rule in place would prevent volunteers from coming forward to help out the council but we don't seem see many volunteers outside of the council as it stands.