If someone uses a slur against you, and calling someone a retard is considered a slur, then you always have the option to report them in the post-game lobby. While you can submit a ticket to Player Support, they will direct you back to using the built-in report system to handle those sorts of situations. It's not that Player Support does not care about the ticket you submitted. It is that they need you, and all other players, to use the correct route of reporting players.
Player Support probably receives thousands of tickets every day, and there are a limited number of support specialists. For them to be able to respond to these tickets promptly, and devote enough time and attention to them, players need to refrain from submitting tickets for things that do not require a ticket. Toxicity is something that Riot spent quite a bit of time developing a very good system to monitor, and it's very easy to use.
So, while Support will gladly accept tickets for spamming if an account is trying to sell elo boosting via private messages, anything that happens in game, or in the pre- and post-game lobbies, they do not need a ticket for. You can simply type "calling players retarded in pre-game lobby/champ select" in the additional comments box when you submit the report for hate-speech.
And because they have such an easy way to submit these reports, and limited time to handle the tickets that they receive, they will often thank you for your report, direct you back to the client and close the ticket. They simply cannot address all those tickets, and still have enough time to handle the situations that actually require the time and attention of a Riot staff member. And there are many situations that do not have an advanced bot system to handle reports; for example any account compromises, chargeback issues, punishment appeals, questions regarding why punishments were issued because the emails were not received, etc. All those things require tickets, and must be handled by the various departments and specialists of Player Support. While some of them will be transferred to different departments, they can begin with those dedicated to player behavior, depending on what happened to initiate the player's contacting Support.
I'm not sure if I've explained it the best, as it's pretty late for me, but I hope I've given you at least some idea why Support doesn't handle all the tickets that can and should be handled by the IFS/client report system. It really isn't because they don't care. It's because they are trying to make sure that all players are given the attention they need.