IMO: The warning system is weak. Riot should deny these players any Influence points for an extended period of time atop of restricting their chat. Maybe then these children would recognize the consequences of their speech.
FE:
1: Warning, no IP for 1 week.
2: Serious Warning, a month.
3: Temp ban, and no IP for three months.
Most of these players don't make any purchases at all, to restrict their progress would influence their practice. It just makes more sense to work the game mechanics this way, and if my idea is too harsh. Riot could utilize the honor / report system further. To where you gain more influence based on honor, and to have a "warning" would reset this...
FE: You need a minimal of 100 conduct honor. All honor adds towards conduct and ea player is initially given the cap... Stacking reports against a player reduces their conduct, and receiving friend and teamwork boosts it. If you've bad conduct you receive no influence points... Say under 50... idk, but what I do know a better system could be made.