Toxic players should just get permanently chat banned instead of permanently banned because they would be able to play the game that they love without ruining other players' experiences.
As others have pointed out, Riot has previously tried what amounted to permanent chat bans, and it didn't work. People under larger-scale restrictions resorted to trolling and intentional feeding, and that was with even a small amount of allotted chat to use. Removing chat outright would doubtless create a similar spike in gameplay misbehavior.
Additionally, people who repeatedly break the rules need to have more serious repercussions to show that they can't just get away with breaking the rules over and over and over ad nauseum. That's why Riot employs permabans; toxic players need to be hammered down if they think they're free to break the rules however they want whenever they want. It's a strict and impactful punishment reserved for the worst offenders or consistent repeat offenders.
Beyond that, I want to break something down in the above snipped sentence;
Toxic players should...be able to play the game that they love without ruining other players' experiences.
If a player is toxic and deliberately ignoring the rules, they don't love the game. If you love the game, it'd be expected that you'd observe the rules instead of breaking them to the point that Riot has to kick you out.
And, on top of that, if a player is toxic, ruining other players' experiences is the point of them being toxic. They have the option to not flame or harass or troll or whatever else, but they do, and it's because they want to ruin other people's experiences.
Toxic behavior is an entirely voluntary thing, and if someone loves the game, they'd be mindful to actually obey the rules so that they can keep playing, and not detract from others' experiences.
Then if someone acted out by running it down mid they deserve to get banned...
You say that like it's that easy. If the past bears repeating, permanent chat bans would result in a sizeable uptick in trolling and intentional feeding - so, to use the Riot Tantram quote KFCeytron brought up;
"...would you rather have more feeders and less negative chat?"
...but for the players that can not stop typing on their keyboard and flaming other people there should be some other type of consequence that does not delete everything that you have done in the specific account forever.
Again; Flaming and other toxic behavior is entirely voluntary. Every player has the option to simply not flame and not harass other people. If they do that over and over and over again, with complete disregard for the rules and the warnings and the punishments they get for doing so, especially the one that explicitly says the next punishment for any misbehavior will be a permanent ban, then honestly, do they really deserve to keep the account?
They don't care about the rules, they don't care about other players, and most of all, they don't care about the game. You could tell them that if they flame even once you'd nuke their account to oblivion, and they'd probably turn right around and flame in the next match just to spite you.
Toxic players are not welcome in League of Legends, and getting an account permanently banned means you'd have to have ignored a lot of perfectly explicit warnings that your behavior was not okay and that further punishments were going to get harsher and harsher.
So much of my gaming life was in that account and it honestly does hurt to have it gone because this has always been my main game that I have always played.
Hate to say it, but, you really should've thought of that before the permanent ban, when you were told that your account was on very thin ice. The warning that came with the 14-day ban couldn't have possibly been more explicit about what was at stake.