This is a theory I've been mulling over for quite awhile. It started by my trying to figure out how the Horn of Valere exactly worked. One thing about RJ's work I always really liked was that he had a very meticulous sense of how the One Power worked, and and how the various -angreal functioned. He also seemed to like just giving us enough hints to figure things out for ourselves, rather than spelling them out. (See the deaths of Galldrian and Taringail) So I figured with something that is supposed to be this important to the story, he'd know exactly what it did, how it did it, and why. After spending probably way too much time on this, this is the conclusion I came to:
Bringing back the Heroes of the Horn to fight was NOT the only thing the Horn is meant to do. I don't even think it's the main purpose of the Horn. I wouldn't call it a side effect exactly, just the one effect that is easiest to communicate its importance to the layman of the WoT universe.
Summoning the Heroes is all well and good, but think about it. The Heroes only number about 100. (And wolves, I did not forget them.) Yes, they are skilled, mighty, and brave. They are NOT invulnerable and invincible. One of them even says straight out in aMoL that they can be defeated. Against all the hordes of Shadowspawn etc, how much of a difference can they TRULY make? Not insignificant, but enough to actually tip the scales? Probably not.
Putting that aside for now, here is something else to consider. When Mat blows the horn in TGH, after it summons the Heroes, other weird things happen, things that are not easily explainable: Rand is standing on clouds above the battle, Rand somehow encounters Ishamael, who seems to mostly stay in dreamshards or Tel'aran'rhiod proper. And the progress of their struggle and the struggle below are linked somehow. How? Why? These questions and the question of how exactly the horn summons the heroes led me to the following theory.
The Horn doesn't exactly summon the Heroes. What it does is somehow either merge or interweave a radius of the current world with Tel'aran'rhod. Perhaps the radius is wherever the soundwaves reach before dying out. I don't have that part worked out yet. This merging is what allows the Heroes to ride and affect the real world. What is ALSO does, it make reality malleable there, much like it is more malleable in the world of dreams. That can explain being in the clouds, it can explain encountering Ba'alzamon, and give some explanation of how Rand's fight with Ba'alzamon can be linked to the Heroes' struggles with the Seanchan.
I also think that this was why it was so important for the Horn to be at the true Last Battle. It seems to be VERY important that reality be malleable when Rand is trying to seal the Bore at Shayol Ghul. I doubt he could have forged all three powers together without it. A fluid reality would also make something like the body swap more likely; Rand and Moridin's sould were already linked somehow by crossing the balefire streams, and Rand was almost remade into Lews Therin when physically in Tel'aran'rhiod at the end of TFoH. (Not exactly the same, I know. But it does let the reader know that such things are at least in the realm of possibility).
I also think that this is why Rand could light his pipe at the end of aMoL. Birgitte saying she needed to leave soon in a scene previous tends to imply that whatever effect the horn has was diminishing, but not yet totally gone. And Rand WAS still in the vicinity.
I do wish I had more info on the Rand part. I know BS won't/can't say how Rand lit his pipe, but I'd love to ask him the following questions, to look at it from another angle:
Is that ability unique to Rand?
Is it a repeatable ability? How repeatable?
Will Rand be able to light his pipe the same way in 10 years? Could he have done it from Tear? Seanchan?
(I suspect most of the answers to be "no".)
I think the only reason the dead Heroes part of the Horn is the main legend is that it is more relatable. Can you imagine trying to explain the World of Dreams to a soldier? A farmer? It's easier to say "Bring the Horn here to have Legendary Heroes fight for you."
I did get to present part of this theory to Brandon Sanderson on his Words of Radiance tour. He said "I'm really fond of that theory. I can't say anything more specific, but it's a REALLY good theory." That makes me think I'm at least on the right track.