...and bans, which only apply to people who speak.
14-day Bans and Permanent Bans don't solely apply to chat-related offenses. Gameplay related-offenses (trolling, intentional feeding, etc.) are met with a 14-day Ban as the first punishment for a verified offense, and more egregious offenses (3rd-party software, account boosting, etc.) are met with permabans, as far as I know.
I suggest, when a person is guilty of feeding too many games, they are forced to replay the tutorial, and then forced to play X number of games in coop vs ai before they can return to pvp.
And how do you define guilty? Do you consider intentional feeding to be guilty, or do you just look at KDA and ignore everything else? If you're looking for intentional feeding and not incidental feeding (or, as it's better known, getting beat), how do you detect it? Have you some fool-proof detection method to tell whether or not someone's intentionally trying to fuck over their teammates?
Or, considering the nature of the punishment, you're probably only seeking to punish people for having bad games rather than actually looking for feeders, since, the way you phrase the punishment, you're punishing people for being "unskilled" (in your subjective view). Do you really think that someone will get better in PVP by doing PVE?
More than that, outside of level/champion pool prerequisites, you really shouldn't force players to play gamemodes they don't want to play. If they don't want to do the Tutorial, you can't force them to. If they want to try and climb in Ranked - as long as they meet the entry requirements, they're fully allowed to do so.
And, of course, to top it off and cement my assumption that you don't actually care about intentional feeders, just players who have a bad match or two:
This would actually decrease the amount of raging that happens in the game because if people knew those game destroyers would get their fair punishment, they would be less likely to verbally harass them.
Why in the fresh hell are you trying to excuse flamers? Nobody should be inclined to harass or flame anyone, regardless of skill. Sure, if someone's intentionally feeding, it's absolutely okay to feel pissed off - but only that far. One shouldn't bring their rage into chat, 'cause it'll only make things worse for everyone else in the match.
It looks like your proposal is less geared towards actually punishing intentional feeders, and more towards punishing players who have a bad game and get flamed for the flamers.
And I could be wrong, but I don't yet see a good reason to assume that this is actually meant to punish feeders. Feeders and trolls wouldn't give two shits about having to replay Tutorials/bots, because they know they'd be able to get right back to trolling and feeding afterwards, and if that's the only punishment - then your proposal would fail to do its job.