Not positive but I think it's because the draft queue and the draft PROCESS takes too long.
I think what they need to do is allow you to prepick your champs, masteries, and runes (per champ), as well as prepick your roles.
So, I click on play now and it automatically loads a normal draft game and enters me into the queue as mid/support. I don't have to touch anything other than the big red button. When I arrive in the game it bans Zed if I'm allowed to ban, selects annie if I'm mid (according to my previous selection, or a preference tree or something) and Talon if I'm support, it also picks my summoners (according to my previous selection with that champ).
Everyone has 5 seconds to change their mind about their picks and bans but they don't have to touch any buttons, it just runs through the process quickly. This whole thing would take 80 seconds from the time you hit lobby to the time you're loading your instance, and you only have to touch an actual button like 10% of the time unless you play a heavily banned champ as first pick (but then it should auto-pick your second pick anyways).
Now, I would say run that system until Plat, and then go back to the start of last season or whatever and give everyone 30 seconds to do everything, but keep the auto masteries etc.
Reason being Plat++ should have some decent and conditional strats, but for bronzies it's an obstacle to actually playing the game.
edit: for instance, today I just played a game with annie mid but I had my adc runes/masteries/summoners from the last time. I don't want to EVER play AD annie. Like, literally I don't want those runes to be an option while I'm playing her.