Hey Darrosh! How's it going?
Actually, before getting to the "why do mooks matter", I think there's a problem explaining why Champions matter. My own head-canon for this is that Champions are kind of like D&D PCs, or Slayers in Buffy: they're empowered by some kind of extraplanar energy that allows them to go above and beyond mortal limits. Put another way, I don't think magic on Runeterra is limited to "mages" as such. I imagine that people sometimes get hit with a surge of power and go Super-Saiyan become Champions, often but not always in the midst of a crisis. So, maybe Lux was a pretty typical mage, and then bam, one day, she power-spikes and becomes a Champion.
In other words, I think that "Champion" is an in-universe term, and not just as a way to refer to people who rep their factions in the League (or whatever happens now post-retcon) or are famous for being skilled fighters. Rather, I think it's pretty obvious in-universe that (say) Garen is not just "a guy who's really good at swordfighting" but a superhuman Champion who could fight his way through dozens of lesser warriors. It would also allow you to have a fight between Caitlyn and Master Yi that wouldn't look like:
https://www.youtube.com/watch?v=7YyBtMxZgQs
It's similar to the headcanon I have for most comic book settings: I assume that part of the "fantasy" of the setting is that chi/ki is real, and spending a decade training with monks in the Himalayas doesn't just teach you some obsolete hand-to-hand fighting skills but turns you into a superhuman warrior. So of course Batman can jump out the window, catch his love interest midair, and absorb the impact of the multi-story drop onto a car without being horribly mangled. There's no RL martial arts technique for surviving that, but in comic book martial arts, all those myths about iron body training or whatever are true. This also explains why some dude can not only get good at punching people, but get SO good that they can fight a dozen gun-wielding thugs bare-handed and win.
I don't think this is that crazy. It just requires the acknowledgement that not all "magic" comes in the form of a person in flowing robes casting a spell from a spellbook.
So why aren't mooks obsolete?
I don't, however, think Champions are so amazingly powerful that they render actual armies obsolete. I've been talking about Warhammer too much lately, but…this was a major theme in Warhammer Fantasy. Heroes were awesome, and could even kill a shocking number of gumby troopers on their own, but the rules made it so that heroes plus mooks were a lot better than just heroes or just mooks.
I assume that Champions lead by example. They're elites who can intervene at critical moments to support the rank-and-file. And very often, in big battles, Champions wind up dueling each other to sort of cancel one another out.
In that Factions update I wrote about the Battle of Shurima, I had Swain comment on this topic:
“How do you kill a hero? You kill everyone else first. Do not waste your time with Champions and Summoners. Your first target will be the Demacian men-at-arms. They are here because their lords have commanded it. They are slaves, and they are already tired. They obey because they are afraid not to. You must give them something more terrifying than the useless pony-riding aristocrats yelling at them not to run away when they set eyes on two veteran Noxian legions flanked by the Executioners and the Nightmare Cavalry.”
Swain stamped his cane into the floor of the gate complex. “I trust you are up to the task!”
Shouts of BLOOD FOR NOXUS and STRENGTH ABOVE ALL filled the room.
—Hextech Revolution Update 9: The HexKorps
Champions are powerful, but they can't actually fight a war single-handedly. Their role in big battles is to inspire the common soldiers and to intervene where their strength will be most valuable.
Could (say) Garen kill a whole squad of Noxian soldiers? Yeah, probably. But if it's Garen and five hundred Demacians against three thousand non-Champion Noxians, the Demacians are almost certainly going to lose. He's not an army. He can try to kill the Noxian commander. He can fight side-by-side in the front ranks and keep Demacian morale up. But there's only so much that a Champion can do. Pretty soon, it's going to be him alone against thousands of Noxians.
So, I think Champions are pretty powerful, but they're not like DBZ characters who can obliterate entire armies with a wave of their hand, and whose only real rivals are other super-mega-energy-blasting-hidden-power-level aliens.