I keep seeing in my Tribunal cases that people report for "he talked **** after game" or "verbal abuse after the game in score screen"

The reason this is not included in tribunal cases and the reason it is rarely looked at is because after the game, you can LEAVE.

You cannot leave in the middle of a game so you are either forced to mute the person or be subjected to their abuse, while after the game you can leave, no one is keeping you there besides you. Stop subjecting yourself to abuse just so you can report someone. Simply requeue and don't let that person get the satisfaction. It's very simple.

On a side note I believe the champ select screen is not included because you can ALSO leave before the game starts with no actual penalty besides a short time before you can requeue. I understand that some people would say "well this causes me a penalty I shouldn't have to endure just because of a troll" true, but you can indeed escape the situation without serious penalty.

While I see what you're saying, the real reasons are technical. Riot is working to include those in the Tribunal but had prioritized the larger changes like the justice reviews and reform cards and honor system.

In my opinion I feel like they shouldn't waste their time. There are other things that could use the attention. I would agree to add pre-game chat but I would NOT agree to add after game chat. To be honest If I see a person be perfectly nice all game then turn into a verbally abusive jerk in after game chat, i would pardon because he ruined no ones in game experience. They personally chose to have it ruined by continuing to read after the game was over and they were able to fully escape the situation.

No, the reason pre/post game chat is because the two chat programs are on different servers and there are programming issues in getting it to automatically load.

Being able to leave is still no excuse to verbally abuse someone.

I find this logic faulty. Do we pardon a murderer if his victim could have walked away before being stabbed? (No, I am not equating verbal abuse with murder, I'm just trying to illustrate that the severity an amoral act is not diminished by any hypothetical action that could have been taken to prevent it.)
By your reasoning, there should't even be an end-of-game chat, because it's nothing but a haven for toxic players to spew whatever bile they want, free of punishment.

I'm sorry but you don't have to read the after game chat. In game chat you kind of have to due to the need to communicate with your team, i personally turn all chat off now because there's no use for it. After game chat is not in game, they did not ruin your in game experience, that is what the tribunal is about. Simply leave after the game. Say "gj team" or whatever you need to say, then leave. If you stop to talk **** to people then you are no better, there are 2 real uses for after game chat, to argue and to say GJ. No need to stay for a long time. Sorry.

and yes stop comparing real life situations to the game it's ridiculous please learn to separate the severity of situations.

honestly I should have watched my wording. The reason I PERSONALLY believe it is not in the tribunal. I do not work for riot so i don't know why. But that is definitely why it's not a main priority, of that im almost completely certain.