Fingon's Nirnaeth Arnoediad

[Maédhros]

He might not have welcomed "help" from Fingon.

Hmm. You may have a point but Fingon and Maedhros have forever being friends.

Moreover in the west Fingon, ever the friend of Maedhros

Take all this together and I don't think it would have done any good for Fingon to order Orodreth to do anything.

Yes, you're right, but if the idea of the Union had come from Fingon instead of Maedhros, would Orodreth or even Thingol would have joined them to form a more united front against Morgoth.
(I'm ignoring the part of the Silmarils, for arguments sake).