I have a strong well thought out argument for why they should make all "normals" draft only. However because this is the internet, I'll get trolled and no one will read it because its too long. However, maybe I'll get lucky and riotnome or some other red will come, read what I have to say and be persuaded by my rhetoric.
You have changed your entire game (s3) to focus on the aspect of your game being something more. You want this game to be a legitimate sporting event, with streamed matches, and teams that have rivalries. You want this esport of yours to grow to be something larger than just another game. However you are committing a vital sin, that has been committed before by professional sports. You are creating a rift between the professional part of your sport an the amateur part.
You are trying to sell players that they too can "go pro". Its a good marketing tactic to use, I should know I teach marketing every day. By having players feel that they might one day be there on the big stage, they play more, spend more, and build the momentum that your company needs to sustain itself. However, the vast majority of games played are not ranked games. People need to practice and take their time to learn, which they do in normal games. However, you have a problem on your hands with players who will play a thousand games in normal, and then jump into ranked and its a whole new learning curve. Its much like people who just play versus bots and then play against live opponents. There are different skill sets to use, and different strategies to employ. You have basically created 2 separate but similar games. Sure some skills are useful in one game and will carry over to others, but many of them do not. Many players have to start over and begin to learn to play the game in a new way.
You want players to stop griefing and trolling ranked? Do you feel like there is any connection between people who do this and people who are simply not ready for ranked because all they have played is normals with blind picks?
The Canadian Football League plays football (and I'm not talking about soccer). However the rules of the game are not quite the same. Much like Arena league and other minor league versions of the game, the rules of the game are similar but not quite the same. There is also a high correlation in mechanics used. A quaterback in the NFL is going to throw the ball much the same ways as those in the CFL. However, you rarely see a star player come from the CFL or Arena league and play pro ball, they have to adjust and its difficult- they often don't make it. However in baseball, you see a strong minor league that plays the same game as the pros. Its a breeding grounds for new stars.
If you want people to take your sport seriously, and you obviously are spending a lot of money on just this goal: you cannot have a minor league that is a shadow of the main league of elite players. You need them to articulate and have a continuum that is seamless.
I enjoy playing normals, and in fact I like playing blind pick, so it seems counter-intuitive for me to want them to change it. However, I would LIKE to play more ranked, but I feel that the skills of counter picking and banning are not strong within the group of people I play with. With no solo queue, you cannot practice as a team very often. If we want to 'go pro' in 3's, we need to practice. If we have to practice against champs that would be otherwise banned, it hurts our ability to play well in ranked. Its like practicing under CFL rules and then having to go play in the NFL.
You said that you do not want to split your base of players, but if you don't give us another option, we will play draft and not blind pick, if its the only option available. If you want this game to be something more than just a game, you have to consider the consequences of having a fracture in the playing base. You don't let us practice drafting, how can we get good? It seems very much the easy choice to have your ranked and non ranked games match up in terms of rules. People can still play custom games if they like, to blind pick or random pick, or whatever.
Your ranked and non ranked need to be the same, otherwise your cannot practice efficiently. Also it doesn't make sense to have different rules for ranked than normal.