[JeffF.]

The battle as described by Tolkien particularly in light of Fondstad's Atlas
of Middle Earth has much that does not make sense and the tactical
deployment is more like a modern battle than a medieval type.

First the distances described in Fonstad's Atlas make no sense. Six miles
separate the Elven wing from the Dwarves and Men. In a medieval battle that
is two separate battles not one. Three miles separate the gate from either
wing. No one would have noticed the gate crashing down and 13 Dwarves
emerging. The numbers stated in the Hobbit (1000 Elf spearmen - bowmen unstated but assumed to be at least as many - and 500 Dwarves). Anyone who has seen an Army battalion on a parade field will see that it takes up a remarkably small amount of space and medieval type mass formations would be very similar.

The geography of the battle needs to shift. The vale between the two arms (southern and eastern) will have to extend closer to the summit until it reaches a fairly narrow area closer to the Gate held by Thorin and his company. This would preclude the ruins of the town of Dale being anywhere near the summit, it could still be between the arms of the mountain but must be farther down. A town of any size being in the middle of a battle with such small numbers would not make sense, it would dominate the battlefield.

The Elf wing and Dwarf/Men wing should be closer together, the ends nearest the other should be within bowshot otherwise there would be no need to occupy both arms. The tactical requirement to man both arms would be to prevent the enemy bowmen from using that adjacent height to support with arrow volleys an attack up the ridge by other forces. If the mountains arms are not within arrow range there would be no point in occupying both.
Another reason for the forces to be closer together is the observes sent by the Free folk to climb the mountain to observe the enemy, these must have been fairly close to communicate with their forces, having such observers several miles away would preclude that particularly given the haste in which deployments were made once Gandalf warned of the enemy approach. If Fonstad's distances are correct such deployments would take hours instead of the short time that apparently passes in the story. Tolkien's deployment of skirmishers to delay the enemy approach also does not make sense, one does not send archers out in a thin screen against cavalry (wolf-riders) and expect them to return. Such a deployment would make sense to draw the larger enemy host between the arms of the mountain where the missile troops of both sides could catch them in a crossfire, another reason to have the arms closer together.

Such distances would make more sense to the narrative description of the battle and Thorin's dramatic entrance.