Drinking and driving is against the law because it puts people lives at risk. Drinking and playing video games is a recommended activity to pursue while drinking because it is safe for everyone. If an adult wants to drink and play a video game I find it hard to justify a punishment. Now I agree you have the right to concern and to express yourself but not at the expense of my beer.
I play worse when I'm distracted by real life or on prescription medication (broke my finger awhile back and the pills made me loopy) than if I had a few beers (even "drunk"). The point is there are an infinite amount of unique circumstances that could affect ones performance in game and trying to police peoples personal life over a video game seems illogical.
Who's gonna determine how many beers is acceptable before a match? Who's gonna tell someone with a medical condition they can not play a video game if they take medication that affects their coordination or alertness? Who's gonna verify the difference between trolling and bluffing (people bluff that they are AFK or throwing all the time and really they are lurking in the bush with vision on you waiting for you to stop moving so they can lunge at you while you are typing)? If you want people to stop playing drunk how could you (or riot) possibly enforce it?
Chat logs don't dictate reality they are just things that are typed many times having nothing to do with the truth. Many times people are drunk and don't type about it or play like they are drunk for a variety or reasons when they are sober. Chat logs and replays are not good enough ways to judge if or how much someone drank and the problem you have seems more chat and trolling specific (someone typing things you didn't like, and an adc with tank masteries and smite) which could also be many other things. Who's gonna pay for everyone worldwide to get a breathalyzer (or more expensively a blood analysis) machine to hook up to your computer to play a free game (I imagine you would half to keep checking after each match as my blood alcohol level changes throughout the night) as so we can verify who's drunk, and who's using drunk as an excuse, and who's trolling using drunk as bait.
Only with answers to these many questions and more could even a framework for moving forward be constructed. Meanwhile there are more pressing issues facing riot staff with more approachable avenues to pursue them (like bringing back item sets or balancing new additions to the game.
Bonus question: what would the riot pop up message say once they magically decided you are to drunk to play?