We don't need the tribunal anymore
I'm not going to argue about the the merits, flaws, ups, downs, or sidewayness of the tribunal. I'm instead going to argue that it is very likely that it is no longer necessary.
Reason: big data.
Simply, after the tribunal has made a few million judgements - one can have a computer act (very nearly exactly) like the tribunal using all of the data they generated. Seeing as people are restricted and banned based on what they say in games, I am guessing this is what Riot is doing. If you want to learn about learn one of the methods to do this, have a youtube link - https://www.youtube.com/watch?v=q6iqI2GIllI - for your perusing/nerding pleasure. With this and similar methods you can teach a computer to recognize many things - from cat videos (very hard) to new exploits or new abuses (medium difficulty, and much, much easier than cat videos - http://xkcd.com/1425/ ), and common abuses are super easy to catch. With this, Riot can eliminate the need for the Tribunal in (reasonable geustimate based on experience, likely higher, but admittedly entirely made up) >95% of cases.
Edit: I'm also going to add that false reports are easy to detect as well. So if people are like "I'm not the #$%^& toxic bro, you are the %^&* ...[All] Report telkie for toxic/feeding/etc GG". The systems could (likely does) easily handle this as well. It could also easily handle people who are not reported for being toxic/feeding/etc as well.
Edit 2: I am in no way associated with Riot (other than playing their game) and know nothing about their actual detection methods. What I do know is a thing or two about how those methods work.