[Kuruharan]

In what sense can the statement "the west was military incapable" be true?

In the obvious one. They could not defeat Sauron by force of arms.

We can speculate that for a good while of the third age, Sauron's enemies (without the one ring) were a match to him.

No, we can’t speculate that because for much of the Third Age they were not contesting him, they just sat back for the most part.

the period it requires them to build an empire, with the help of the One Ring, necessary to contend Sauron

Exactly, they didn’t have that.

It can even be argued that the gathering of strength can be hastened by claiming soldiers who obey Sauron's power

This has always been a bit of an unclear issue. The Men that followed Sauron (and there were probably plenty enough of these to do the job) were probably not in thrall to the power of the Ring to any large extent. I think they could be counted on to follow Sauron regardless, if for no other reason than the new ringlord, whoever it would be, would be representing something they had hated and fought against for generations.

The orcs, I have to admit, I’m not sure about. On the whole I’m inclined to think they would also continue to follow Sauron for similar reasons to the Men. Whether they could actually attempt to actively harm the new ringlord I think is largely irrelevant. All the orcs would be there for is to help kill the enemy soldiers. Sauron would deal with the new ringlord.

Tolkien noted that the nazgul wouldn't be wholly invulnerable to the power of an enemy ringlord, even in the case of Frodo; I would guess that the hosts of Mordor would too be vulnerable to its influence

But Sauron would remain their master. That is not called into question in the case of the Nazgul, they remain Sauron’s slaves. They would not be needed to deal with the new ringlord. They would be much more effective doing nasty things to the new ringlord’s army.

But regardless of this, this little debate is a waste of time. It was relentlessly stated in the books over and over from the time of the Council of Elrond that the West could not hope to defeat Sauron militarily. The West also utterly lacked the capacity to launch effective offensive actions against Sauron, that in itself is very telling. I find that your argument has no foundation.

I believe that at the end of the third age, Sauron can be defeated in a direct battle.

By Gandalf, nobody else. Saruman couldn’t master the Ring to face Sauron (as the rotting horse corpse lying over there that I’ve had to beat mercilessly for the past few months attests to). Galadriel and Elrond were not of the same order of creation as Sauron and for a number of other reasons just don’t stack up. Aragorn is explicitly denied the ability to best Sauron in such a situation.

I don't know what else there is to say about this.