The civilization tree is, perhaps, a little too essential for everything - it's necessary to get .. well, every single resource in the game except mana. Your population (growth+food) and therefore your research/gold is capped by how far you get in civilization, your production is multiplied by how many appropriate civ techs you have, even metal, influence, etc. all come from civilization techs. You can't do anything without this tree, it's a no brainer.
That being said, the civilization tree gives you next to nothing to actually win battles with, so you can't do anything with just this tree either, and that's where the other two come in. You have a choice of war or magic - trained units or champions, basically - and both ways work, I've tried.
The magic tree does need some work though; while it's viable to win games with nothing but magic+champions and few if any warfare techs, most of the magic tree isn't really necessary or practical to get - all you really need is the final champion recruiting tech (breon's letters? something like that) and then you can abandon the magic tree, which is good because you need tons of civilization techs to a.) get enough research to reach the final champion recruiting tech, and b.) get enough gold to recruit those champions.
So anyway, there are really only two paths: civilization+warfare or civilization+magic, with civ being far too essential for anyone but unable to stand alone. And the magic/champion path to victory is really a dedicated civilization path, except with a little bit of the magic tech tree thrown in to let you recruit champions and do quests. It's not that the rest of the magic tree is useless, it's that your champions and spells are fine without it, and you can't afford it without filling out the civ tree first, by which point the game is over. Warfare has a similar problem to a lesser extent - while the entire tree is useful, you just can't afford to research it, or to build the units it gives you, without filling out the civ tree for research/production/gold bonuses, and the game is probably over before you can do that and get back to finishing the warfare tree.