[JeffF.]

It does not appear that the Balrog was in Sauron's service during the War of the Ring nor does it appear to be that he ruled over the Orcs and Cave-trolls within Moria. These inhabitants are in several places described as Servants of Sauron but they were obviously intimidated by the Balrog whenever he chose to appear. This is reinforced in the RotK Appendices in Durin's Folk the orc Azog commanded the orc army out of Moria that fought the final battle of the War of Orcs and Dwarves, though the Balrog was a spectator at the Gate and was seen by Dain it did not participate not even as a commander.

Perhaps one reason is that the Balrog could not be trusted in that if it found the One Ring he would undoubtedly use it to become a new Dark Lord rather than return it to Sauron. Despite all this the Balrog could have been militarily useful to Sauron. Sauron's forces in Dol Guldor with those of Moria seemed to be intended to tie down the Elven forces of Lothlorien (Galadriel & Celeborn) and Greenwood (Thranduil). In modern terms they were an 'economy of force' army. I say this because they were repulsed three times from Lorien and decisively beaten by Thranduil so obviously lacked the power to overcome either Silvan Elf Army. The objective of the Dol Guldor / Moria orcs was probably to prevent the Woodmen and Thranduil's Elves from assisting the Men of Dale and Dwarves of Erebor in their defense against the Easterling invasion and to do this they would have to attack both Silvan Elf realms otherwise the un-engaged Elves would attack the rear. The Balrog could have been of great assistance in this mission. It was said that Lothlorien had the power to resist any enemy unless Sauron himself should come there so perhaps even the Balrog could not overcome Galadriel but it is likely that it would have been decisive against Thranduil's elves who were not protected by any similar power to Galadriel's. Had the 'main effort' of the Dol Guldor force been sent under the Balrog against Thranduil they likely would have routed the elves and if joined to the Easterlings perhaps even would have overthrown the Dwarf defenses of Erebor. If this success was achieved at the cost of the orc army sent against Lothlorien being destroyed it would have been well worth it if the entire North were conquered.

The Balrog seemed very similar in power to the Lord of the Nazgul and could have been served as a second great captain for the Dark Lord. It's 'historical' demise also brought down Gandalf the Grey and would seem to have been a good exchange since it eliminated the most powerful being fighting for the Free Peoples but in retrospect since Gandalf was resurrected in a more powerful state than before the death of the Balrog was not worth its loss.