It would be great if factions were more relevant. But like the others have said, I don't think in-game buffs are the way to go.
Instead, they could have a new out-of-game mechanic, let's call it Faction Points.
Two possible ways this could work...
Option 1, Pick your faction. Whenever you play as a Champion from your faction, you get Faction Points in addition to Mastery Points (one for one).
Faction Points would have two purposes. Individually, reaching certain amounts of Faction Points would give you access to (or discounts on) special skins or other cosmetics. Community-wide, the total number of Faction Points combined from every player of that faction would be used to determine how much influence or power that faction has at the moment. Then they could have a map or something that's updated every week or every patch to show the current balance of power in Runeterra.
If they wanted to take that a step further, they include how well specific factions performed against each other. I assume they already monitor win-loss stats for every Champion. Well, that information could be broken down by faction to look for trends. Like, if Freljordi Champions are doing very well against Demacian Champions, maybe there was a major raid or something.
Changing factions would be a difficult process. Say, you'd first need to somehow indicate that you are trying to change factions. Then, you would get Faction Points for your new faction, but you would not be considered aligned with that faction until you reach a certain high amount.
[Bonus, Riot could adjust the weekly Champion rotation system so instead of having ten Champions to choose from, you'd have ten (the same ten as everyone) plus one more that only players from your faction can pick. So every week would have ten Everyone Champions plus one Demacian Only Champion plus one Ionian Only Champion plus one Void Only Champion, etc.]
Option 2, Faction determined by performance. Similar to Mastery Points, you would earn Faction Points with every Champion in every game. The faction you have the most points with is the one you are aligned with. So if you want to be associated with the Demacian faction, you would need to play most of your games as Demacian Champions, otherwise you will find yourself aligned with someone else.
This could include the same community-wide tallying as described above.
As an aside, if they ever do introduce a new focus on factions, it would be great to introduce a game mode for faction-specific battles where each side draws their Champions from a single faction.
