If I understand it correctly, Amazon's argument here appears to be that the NLRB's statutory authority (i.e., its power to adjudicate labor disputes) is essentially unconstitutional, as it deprives Amazon (and other companies) of the ordinary trial process.
If this interpretation is correct, the consequences are disturbing: a ruling against the NLRB here would imply absolute judicial supremacy, and not a system of checks and balances. In effect, it'd break the US Government's regulatory backbone: any regulatory decision could be challenged not within its statutory limits (or for exceeding its statutory limits), but on the basis of statutory regulation itself being unconstitutional. In effect, it would amount to a government whose regulatory framework is not controlled by the elected branches, but by the sole unelected one.
If this interpretation is correct, the consequences are disturbing: a ruling against the NLRB here would imply absolute judicial supremacy, and not a system of checks and balances. In effect, it'd break the US Government's regulatory backbone: any regulatory decision could be challenged not within its statutory limits (or for exceeding its statutory limits), but on the basis of statutory regulation itself being unconstitutional. In effect, it would amount to a government whose regulatory framework is not controlled by the elected branches, but by the sole unelected one.