You're mistaken on two points: Bard doesn't support Ionia in any special way and the battle on the Bard's Mountain home was a battle fought between a bunch of peaceful settlers and an invasion force from Noxus. They were civilians and you're using them to judge a nation's fighting worth when the likes of Irelia, Yi and Lee Sin exist, and they have artifacts like that egg that can cut mountains in half?
Also what the hell does Ionia not count towards? It's an island nation. Aside from a few rogue elements a lot of its representing champions will fight to protect it, along with its populace. It's not like there's only two samurai, one monk and one qualified archer; they've been honing their martial prowess for centuries.
Noxus and Demacia are an empire and a kingdom, and are not wholly unified. Nowhere is. Demacia's got a pretty structured government but they still do conscription and indoctrination, which wouldn't really be necessary if everyone was all about the cause and what not. In Noxus people kill each other daily. Swain became Grand General by murdering his opposition. Hardly a place that's got all its shit together; Swain's just the man able to keep things rolling for now.
And if we look at Noxus and Demacia and how they'd fair against other nations, tell me how they would beat the Shadow Isles with monsters like Mordekaiser and Hecarim roaming around? How would they even compare to the Ascended of Shurima? Just one of those guys could take on hundreds, perhaps thousands of soldiers with their god like powers. Freljord's a nation where if you can't fight you'll die no matter what, and they not only have strong warriors but brutish species like the Yetis, Ursine and Trolls that can just as easily fight back, even considering that Freljord's a divided nation.
This shit's not black and white mate; Demacia and Noxus aren't the centerpieces of Runeterra, far from it. They're two parts of a much larger world and they haven't even begun to impact history to the level that nations like Shurima and Freljord have, or individual entities like Aatrox and Bard have.