I appreciate you taking the time to post, but I'm genuinely a little confused as to what you're saying.
they are actually pretty intense but the admin figure that each match has X weight based on Y players who focus on Z faction.
I'm not sure I follow. The weight of a match is set based on the relative skill matchups of the Summoners on each side, and the relative standings of the two factions. A stomp by a bunch of Golds against a bunch of Silvers is worth fewer points than an even match, and likewise the dominant faction beating the weakest faction is worth fewer points than a match between two factions that are neck-and-neck. The latter adjust is somewhat arbitrary, and is just meant to encourage occasional brawls between the champs and the underdogs. The former has a pretty strong empirical basis in observed winrates.
The faction members each voted for A B or C to have happened and depending on the vote the point value for the match is distributed among A B and C.
Point values for matches are not "distributed", except between the winner and the loser. Is this maybe an allusion to World Systems?
Not to mention that at any given time you have approximately 9 players (counting you) that want to play but they are distributed across 3-5 factions so no one actually wants to play.
We are always looking for more people so as to make it easier to get a match going, but I think your characterization of the situation is a little pessimistic. At a glance, there have been about 200 matches in the past ~70 days, or about 3 matches per day. Not that we don't want to increase that number, but I think we're doing alright so far.
Then there is subbing for a faction where you can help one of your enemy factions but your participation is only weighed at a fraction of the standard value.
This is primarily a way to make matches easier to start: if necessary to fill in some open slots on a team, a faction can bring in subs from another faction, so long as the subs aren't playing against their "real" faction. So, if Noxus and Shurima are setting up a match, and Noxus still needs two more Summoners, they can bring in two Piltovians to round out the match. These matches are worth fewer points because the fate of a faction is supposed to depend on what its Summoners do. For example, the rule is set up to "zero out" if either side is entirely made up of subs: it would be really weird (and unfair) if, e.g., Demacia lost points from a match that had no Demacian Summoners in it.
It sounds like overall you think the rules that govern Factions are too complicated. That's a fair critique. We certainly would prefer for things to be simpler. If you have a concrete suggestion for how to simplify the rules, I'd certainly be game to hear it.