I'm honestly not sure what you're suggesting here. I understand that Garen is, in many ways, the iconic Demacian figure but he also isn't the only Demacian in the League. Shyvana's principle relationship is with Jarvan and her lore focuses on them, rather than involving another character who played no real part in bringing her to the Institute. This really makes about as much sense as complaining that Lux didn't appear in her background.
Shyvana and Garen don't exactly see eye-to-eye anyway. To quote RiotRunaan:
"Garen ... finds Shyvana to lack the principles that truly make a Demacian warrior. He values discipline and self-control, and in his mind, Shyvana exemplifies none of this. He'll fight beside her, but he may disapprove of her methods".
Trydamere's lore, in the utterly literal sense, has absolutely nothing to do with his marriage. Said marriage though was born, in no small part, because both parties desired the protection and stability offered by becoming an Institute protectorate. Their union served to legitimise Freljord on the political stage and paid dividends for both of them. I'm honestly not sure what the "problem" is here.
Anivia is a spirit of elemental balance and most certainly does negotiate with others. You're really just forcing your own ideas about who the character should be, rather than actually using the information Riot has given us.
Of course Sejuani has great synergy with Ashe: They're both descendants of the same bloodline. If I was being particularly generous, and I really don't feel this way, I'd even suggest that you could take that as an element of satire about how well the two of them could work together, if only they would put aside their quarrel.
As for Volibear, we have no idea how many ursine there are, how well matched they would be in any actual war or what the prophesy he saw was pertaining to. Again, you're just saying "This should work this way" without any regard for the way the developers have chosen to play their hand. Why would they want to take over Freljord?
If you want to approach this from an utterly lore-friendly angle: That'd be the summoner's fault, wouldn't it?
I'm also not sure what your point is here. Combat in the League is far from a truly fair fight and features characters with a huge range of esoteric skills and disciplines. Why would a mere master swordsman, of only one city-state, be anything exceptional?
I think that the OP meant that we don't see much interaction between the lore and the actual characters?
Yeah, I agree he's being too ragy, but he does have a point, maybe reformulate the post?
Also, It's from the fact that we lack few pieces of info that we may go conspiring within our minds, Volibear could be the exact case: Nobody knows how large or small is his group.
@OP = fix w/e you're trying to say, and try to be more clear with your words, maybe? Somehow, the rage factor is overlaping everything else on your words.