Battles of the late Third Age

[Kuruharan]

I think you are on to something here. However, I might take it a step farther.

Rohan on the other had permanent settlements that required defending (Settlement of westfold, Meduseld and Helmsdeep etc).

I think that the Rohirrim were semi-nomadic to a degree. Yes, they had permanent settlements, but I kind of think of them as being a people who moved about some with their horse herds. I picture them as kind of in a similar vein to the cattle drives of the American West, if you'll grant me the loose comparison.

Now, admittedly, there is really no evidence of this except the lifestyle of their kin in Rhovanion back in the day, but I kind of enjoy the picture.

In Tolkien's world the heavy infantry non-par excellence was the Gondorian infantry.

I disagree with this. Or at least I would question what your source for this is.(Ignoring for the moment what the Gondorian army was actually like because that opens up, say it with me now, "a whole other can o' worms" about what Gondor's military and defensive structure was actually like). The statement seems to me to ignore too much.

As an example of a potential example of other heavy infantry, and I realize that I am probably going to raise some eyebrows here by bucking a long held fantasy assumption, but I don't think that just because Wood Elves lived in the woods meant that they did not have heavy infantry. I point to the large numbers of elven spearmen at the Battle of Five Armies. I think they were at least "heavyish."

And, well, then...*cough* (how to say this without seeming like a homer) what about the dwarves? However, they don't seem to have fought on the plains too much.

*EDIT* I forgot the Battle of Unnumbered Tears.

Then there were the heavily armored axe-men-orcs that Saruman used...

The fact that the Rohirrim was lacking both infantry and artillery and possessed only light cavalry goes to show how deficient the army was.

As it is presented in the books it could certainly be a bit problematic. However, if the Rohirrim would go all out for horse archers that would change the situation a bit.

(Full disclosure time here: I should say that I personally believe that a well armed horse archer was the most effective type of fighter prior to the advent of gunpowder.)