"But One and not the Greatest"

[Angry Hill Troll]

When Frodo, Sam, and Gollum see the Army of the Witch King issuing from Minas Morgul, the text says that

So great an army had never issued from that vale since the days of Isildur's might; no host so fell and strong in arms had yet assailed the Fords of Anduin; and yet it was but one and not the greatest of the hosts that Mordor now sent forth.

The point of the wording, I suppose, is to impress upon the reader just how much military force Sauron had amassed. But it raises a few questions of how well thought out his strategy was:

Given that Sauron was sending a greater army into the field at the same time, where was it going? Who was commanding it? It would make the most sense for Sauron to send his greatest force against Minas Tirith, which after all was the most populated and best fortified stronghold of his enemies, and also the closest to Mordor.

As it turned out, the force he sent wasn't quite enough to get the job done, once the Rohirrim showed up and Aragorn commandeered the fleet of the Corsairs.

So what was Sauron's greatest army doing? The only thing that seems even remotely plausible would be attacking Lothlorien, but as it turned out this would have proved pointless, since for Lorien to be overcome a supernatural force (e.g. Sauron in person) would be required.

And if the Witch King wasn't commanding the greatest army, who was? Clearly the WK was Sauron's most capable servant (as stated by Gandalf, and evidenced by the WK's being put in charge of the hunt for the Ring). So why wasn't Sauron putting his top lieutenant in charge of his greatest army?

Sauron seems to have given the good guys some breathing room by not putting all those forces to particularly effective use...