Yeah, I agree that the "New Player Experience" is definitely something that needs to be looked over and worked on. The game itself already has a pretty big learning curve compared to other games, but the icing on the cake that turns off new players, from what I've seen, heard, and experienced is that the community itself.
The community is easily the main culprit for why the "New Player Experience" sucks in League, with the game's mechanics being the secondary reason. The League of Legends community has a reputation of being the most toxic gaming community in all of gaming. It's filled with people who are ready and able to insult others for not playing the way they want the other player to play (even in ARAM), there are people who are ready to tell others to kill themselves in the game for making one bad player, etc.
Riot should really take a more critical stand on their community to ensure that the community is open to everyone, especially new players. They've already done a somewhat okay job at the tutorial and trying to ease new players into the game, but the one thing that they barely put any effort into improving is improving the community's behavior.
The League community has earned the reputation of being the most toxic gaming community ever, and they will always retain that reputation. From what I've seen on these forums, people who get permanently banned have very little to no resistance in making a new account, and if they dumped time and money into their permanently banned account, they probably don't care if the new account gets banned because they don't have an intimate connection with the account, they can just make another one and continue being toxic.
The New Player Experience will never get any better until the community's attitude improves.