Riot actually has a lot of data to back up the current 4-strike system. Back when Tribunal was active, there were a lot more tiers of punishment, and they didn't always bump a player a tier with each punishment. There was something like 7 different punishment levels available (this was before they implemented chat restrictions, so all were increasing-length time bans).
What they found was that a vast majority of players corrected their behavior after just the initial warning. Then a vast majority of the remaining ones would get the point after their first time ban, etc. After even just 2-3 punishment tiers, pretty much everybody that was willing to reform had done so. Once they reached a point, reform rates dropped off significantly, to where almost no players were actually reforming. The only thing having tons of punishment tiers did was delay the amount of time before players who were clearly not willing to reform would actually reach their permaban, thereby allowing them to continue ruining more and more games while just waiting to work through the rest of the system up to a permaban.
It was largely based on that data that they worked out the current 4-tier system. By the time somebody is reaching a 4th punishment, their chances of reforming are so low that their okay with just issuing a permaban.