How to teach league
Its the same as in other disciplines. You teach by removing complexity and providing opportunity for learning fundamentals. Streamers should start finding champions whos gameplay centers around an aspect of league and teach those elements.
For instance, I learned cooldown based gameplay from playing ekko. You can learn split pushing with shen. You can learn kiting with Ashe. If I had to teach league, I would help my student create some good rune pages for these three champions (remove that complexity) and I would choose these champions because I could have a specific lesson in mind when teaching them.
For ashe, have them practice animation canceling on the farm for 10 minutes, and then work with them on kiting in the mid game which is hardest. The objective is to get the student to understand that bruisers will turn and run from you in the mid game if you kite them well with w. The idea is that you dont need to aggressively kill them with kiting, you need to waste their time when they are targeting you. Its better to try and openly kill a bruiser only after they are attacking someone else on your team.
For ekko, I would remove complexity by helping my student get the cdr page you need for his gameplay. A lot of people might take a different ap rune page, but cdr is huge for him and a new player might not realize that. I would teach him what type of laning style will make your opponent burn abilities on the wave instead of you and help him think about going in when ability is on cooldown and making sure his cooldowns are ready in time. It might even be instructive to have the player experience a game without the cdr runes to understand how longer cooldowns can hurt you. If you can understand the mentality of your laning opponent from the perspective of cooldown based gameplay, youve learned something about the game. If you dont understand this gameplay, you might not realize that player A is saving an ability for you and you will need to wait for that ability to become burned before you can go for an outplay.
For shen, you can learn to watch the rest of the map while you split or even for the whole game. The ulti plays shen makes are perfect for teaching and practicing map awareness.
Each of these champs has a core gameplay that makes them work and sort of covers the breadth of league gameplay. Thats why I would pick them, but I dont see streamers approaching teaching like this. I see them offering general statements, Tier List focused advice, and cliches. They dont ever offer "learning objectives".
With the students in the lab I am teaching, I often have to give them a task in order for them to learn. I said last night "Go and build a linked list that looks like this". If I was teaching league I would say, "Go into a custom game with a friend who owns Yasuo and take Ekko against him with mana regen mastery, cdr mastery, thunderlords, your cdr page, and ignite. Beat him by playing safely and backing for a second dorans ring. Once you have dorans ring, use your q to clear a wave and simultaneously pop his shield. When his sheild is down, force him to use windwall. Become good at getting to this point. It should cost you the minimal ammount of HP and mana to get to the point in lane where his shield is down, his windwall is down, and there arent many of those dangerous minions around. You have the advantage. Dont get knocked up." Thats a lot to ask, but if you can do that solo against a yasuo player, you understand how to play the cooldown game, regardless of your farm numbers and so meeting that objective implies that lessons are learned.