I do not know of a single US company that does not allow workers (employees) on the board.
Technically, if a CEO is on the board, then a company’s employee is on the board. Shareholders will probably not vote to put a line level employee on the board, though.
Technically, if a CEO is on the board, then a company’s employee is on the board. Shareholders will probably not vote to put a line level employee on the board, though.