It would make sense, after all. The Heroes are spun out as the Pattern needs them, just like the Dragon. There is something that is permanent in all the lives that they live (e.g., Birgitte's always an archer-type), just like the Dragon. They are also reborn at particular times (e.g., Gaidal before Birgitte), again like the Dragon.

It also makes sense that LTT doesn't appear when the Horn is used by Mat - LTT's already been reborn as Rand!

The odd thing is that when you look at the people called by the Horn, none of them are channelers. There's swordsmen and -women, there's an archer - all skilled warrior-types with hand-to-hand or weapons skills. Hawkwing even says that Hurin might become a Hero bound to the Horn. Yet despite the fact that Birgitte's arrows strike like lightning, there's no sign that any of those plucky Heroes can use the One Power...