Permabans are the reason this game is so toxic...
I sincerely doubt it. With toxicity being a problem in games that are more lenient with punishments/permabans (WoW, SMITE, etc.), you'd have to have a hell of a lot of evidence to support the argument that permabans are the reason that League is toxic.
Perhaps maybe have an option to permaban someone’s chat restriction so they can’t say bad things anymore.
Riot has tried what amounted to permanent chat restrictions before; moreover, indefinitely scaling chat restrictions. People under these longer-scale restrictions either used all of their allotted chat for extreme toxicity, or resorted to trolling or intentionally feeding because they couldn't say bad things anymore.
And I genuinely doubt you'd want to risk an uptick in trolling/feeding cases just to spare a scant few toxic players from being permanently banned.
My friends get permabanned because they say cuss words.
Correction; your friends got permabanned because they harassed and flamed and were generally toxic. Swearing is fine; leveling swears at other players isn't. It's the difference between "aw fuck, that went bad" and "you fucking piece of shit".
Yet there’s all these players who actually script and cheat in the game. And they still play on multiple accounts.
Scripts and cheaters are typically punished in vast ban-waves so that the people who make those scripts/cheats can't figure out what tripped the detection system. Keep an eye on the PB board long enough, and you'll typically see the aftereffects of a ban wave.
Regardless; other people breaking the rules is not a valid excuse for anyone to go breaking the rules themselves. Unless you can find a clause in the ToU that says something along the lines of "the presence of these rules is void if found and proven to be broken by another player first".
Permaban is obviously not a good solution, if it was, the games would be less toxic and it’s not. It’s worse now than it ever was.
I've frankly seen toxicity decline over the past few years. I don't know about you, but League used to be downright awful a few years ago, and now it's tolerable. There's still of course ample toxicity, which sucks, but that's doubtless because of a slew of issues, rather than it being because Riot permabans accounts.
I really think the better idea is to IP ban or chat restrict forever so these players stop making new accounts and making it harder for low levels.
Neither of those solutions would work - as mentioned before, permanent chat restrictions would just result in more trolls and intentional feeders, whereas IP bans are easily circumvented, and they could cause serious collateral damage considering shared networking spaces (like college dormitories, internet cafe's, etc.)