To say there is not enough information in Tolkien to create a reasonable, defensible scenario from is to give Herodotus and Thucydides and Livy a free pass. Of course, archaeology and further scholarship may improve our knowledge of ancient battles, but we will never more know about the military history of Middle Earth than we know, except as it is informed by understand real history.
So did that poll even ask the right question? With Middle Earth, as with the bronze age, you have the info you have, the question of whether or not you *feel* you have enough info for a satisfying game is a question of what makes you feel that way, not what is necessary.
You have to go pretty late in history before you can say with any degree of certainty that you have the numbers, types, condition, and disposition for any given battle. You have that for some battles in the eighteen century, and probably most battles in the 20th, but we do want to wargame some things before the Age of Reason.
ponders getting some of his 28mm fantasy figures off the shelves and onto the tabletop.