Ok, our Rules Gurus may have something to add, but since there's nothing stating that you can only play him at an Underground site, I guess you COULD play him at any site, but as you said, he'd be instantly discarded. Also, if you play him at an underground site and the Fellowship moves to a non-underground site, it bites the dust.
Now, you wanted a reason as to why playing it at a non-underground site? Perhaps the Free Peoples player just added a ton of twilight and you want to discard another card to try and reconcile for a better hand for your Free PEoples turn, then you could play the Balrog AND discard another dead card, cycling 2 cards instead of 1.