The NLRB is an independent agency of the US Government, which means that its power derives from the statutory authority of Congress. That's what makes it controlled by one of the elected branches.
(The argument is not that the NLRB itself is elected, or needs to be. It's whether the judicial branch has the authority to diminish Congress or the Executive's statutory authorities as enumerated under the constitution.)
(The argument is not that the NLRB itself is elected, or needs to be. It's whether the judicial branch has the authority to diminish Congress or the Executive's statutory authorities as enumerated under the constitution.)