I can't 
-tee that rito will actually update their several season old tutorial, but it would be nice to have one in Summoners RIft, since, most games are played in Summoners Rift.
I believe that for a new player to even consider taking the time to actually do the tutorials, there should be a reasonable reward for doing each one. Like an 'Exp boost for 5 games' (this would make perfect sense, because it allows you to climb levels faster since you actually took the time to educate yourself by taking the tutorial). Plus, it should be prompted that they will get a reward for taking the tutorial, instead of 'surprising' them with the reward after. Personally, I would like to know that I'm not doing the tutorial and getting nothing special from it.
Here is my idea about Role-playing (pun intended)
Adc:
They have you open shop and buy the recommended starter items.
They teach you the concept of last-hitting: (the game will 'freeze time' and point out the minions with low health and tell you to auto it).
-also mention the value of each minion: melee, castor and cannon
Have you Attack move and show you the auto range of your champion and advise to maintain roughly that distance from enemy champions.
-this way, you have a general idea about postioning as an adc and even kiting (because you were told to maintain the distance, so you would have to back-step to do so)
--there could even be a brief description of kiting itself (they could make it easy for first-time kiters to practice this mechanic by playing Ashe with Q proced and giving them 
and have a slow melee champ run towards them and only auto attacking them.
Support:
Playing as 
would be good for new players, because she only has 1 skill shot, and provides a poke, heal, speed boost, and CC.
These terms can be taught:
Poking/Trading: Show Q range and use it, point out the creeps' aggro and note that it is important to retreat behind castors immediately after poking for most cases.
Healing: The adc's health is low, so Sona heals them. "A healthy adc, is a happy adc."
Buffs/Debuffs:
Speed boost:
-Offense: for closing in (so adc can get another auto in)
-Defense: to help the adc get away
Example: Have use E to close in on enemy champ, and hitting E procs her passive so that her next auto slows the enemy champ. that will explain the buff for and her nearby allies and the debuff used on the enemy.
Peeling:
Explain CC (Crowd Control) This could by sub-categorized under 'Debuffs' in a way.
Offense: Ult to lock down the enemy when he is low so your adc can secure the kill
Defense: have the enemy jungler come in from river and both the support and adc can start running towards tower, once the enemies get too close, freeze frame for a moment and show that the enemies are close enough together to line up a good Ult.
Show the different forms of CC for peeling: like 
's knock up and knock back, 
's stun, 
's pull and silence, etc.
Mid:
Reiterate the importance of Poking, Trading, CC and pushing/freezing for this role.
would be a good candidate for new players learning mid, because since she depends on her Passive so much, this will also help new players see the importance of Passives in general and also look into the passives of other champions.
Have a 
show pings to briefly illustrate the importance of communication. For the mid tutorial, he could be signaling that he is on his way to gank mid:
-briefly reiterate 'Ganking'
then once target pings the enemy mid, then could ult/stun the enemy mid and do her burst, while goes in.
Top:
Fighter and Tank:
would be easy enough to explain both.
Show different full builds for each the fighter and the Tank
Also show 2 different builds for extremes in AD or AP damage in the enemy team:
Show the Tab screen and point out the enemy builds and explain that they are all AD or AP. So it will explain why has the build that he has.
This in itself is very vital for every game for new players to know; to check the enemy's build so they can be aware of so many factors:
Who is doing damage
What kind of damage is being put out
Who is the tank
Get an idea of what build path they are going for based on the items they have so far... like if someone has 
, 
, and 
, ...WHAT DOES THAT TELL YOU?
Then show how the Fighter/Tank is important in a small team fight (like a 2v1 against the ally adc, then comes in and front-lines while the adc attacks from the back)
Jungler (tutorial unlocked once 
is unlocked)
is probably the easiest candidate for new players to learn Jungling.
There could even be a whole tutorial on and smite items all in itself, because there is so much to cover...
Show all the monsters, their stats, and the buffs from smiting them (this will show new players how they should go about through the jungle, and generally in what order.
Leashing: Show a basic leash. for Gromp and for Crugs.
Ganking: show the minimap and explain who most likely NEEDS a gank.
Holding a Lane: show that the mid laner pings assistance in lane as he/she recalls. Then show the jungler going to mid lane and pushing the lane generally halfway between his and the enemy's towers... or simply clear a wave and quickly proceed to jungling.
NOTE: So that we are on the same page, I started off visualizing this as the new player hands-on playing the role when I started typing this with the adc, then I realized that it would be better if they were videos of people doing this, like in-game scenarios, having the video showing a game paused at points and explaining what just happened, what is going on now, and what is going to happen. Plus, there could be arrows drawn out and different illustrations outside of the game in the video to give the player a clear idea of what's going on.
There is really so much a new player needs to know... especially now. Even if you know all the basics of plaything the game, you still need to know what all the champs do... and the only way to do that is to play games AGAINST them as well as playing games AS them. Once they start building knowledge of all the champions, this will help them develop team synergy, team fights, counters, timing initiations, and much, much more.
I'm not entirely sure HOW rito should update their Tutorial, but I still think that they really SHOULD.
