It feels very much like riot is handing out penalties for pretty much minimal cases.
If you're getting punished for an ostensibly minor offense, then it'd probably do you well to consider just how frequently you commit that offense; since the IFS works off of Severity & Consistency, continual low-key offenses (such as passive-aggressiveness, defeatism, etc.) will eventually earn the same punishment as more severe ones (like flaming, insults, etc.)
Everyone, you and I included get upset sometimes. It happens, despite what HALF the pretentious commenters on this specific sub forum would like you to believe.
I hardly ever, if ever, see anyone say that people don't get upset or shouldn't get upset. We acknowledge that people do get upset, but what we reiterate is that you shouldn't let that vitriol spill over into chat.
will this physically hurt the other person or mentally?
Words on the internet cannot directly, physically hurt someone.
Even still, your flow chart is too sparing. Where's the consideration for the harm to team cohesion? Where's the consideration for the rules? Why is psychological harm the say-all/end-all for whether or not something should be punishable?
What would the mute function be for if not to just ignore a persons comments.
The mute feature is there to prevent you from seeing further chat from someone in the context of a given match; whether it be because they're agitating you, harassing you, etc.
The report feature, as Imperial Pandaa said, is there to prevent other people from having to deal with it in future matches. It's meant to rectify the player's behavior and encourage them to stop agitating/harassing others.
It makes very little sense to be so quick to punish others when there are other things implemented to make the experience better
The rules > mitigating features. Everyone agrees to follow the rules Riot set up in the ToU. IMO, it makes very little sense for people to be so eager to break the rules.
And, as ever, there's appropriate analogies for mitigating features and rules/laws, two examples of which;
Bulletproof vests exist, and there are still rules against running around and shooting people.
Fire extinguishers exist, and arson is still a crime.
The existence of a mitigating feature does not supercede the rules against those offenses. And since the rules exist, it makes perfect sense to punish people who break them.