Say, for example the chairman of an organization that works with kids is also the founder of the organization and also serves as the main employee working one on one with the kids, should that person forfeit their position on the board to be compensated for their time in that capacity?

Board members of a 501(c)(3) should not receive any compensation from the organization. They may be compensated for out-of-pocket expenses, but may not be paid for their time. If this person is an employee he must either (a) resign from the board or (b) agree to work for free. Reason is that the board is ultimately responsible for hiring and firing decisions, and if a board member is an employee then there is a major conflict of interest.