I just want to bump this topic as I was considering writing the same topic. This option is straightforward to develop and implement. It would dramatically improve the game-play experience for most players. Sure, queuing for games might take a few extra minutes as the supply and demand for certain positions (like support) is not exactly equal, however, I believe that players would much rather spend an extra few minutes in queue than have to risk arguments in champion select/trolls/people unhappy or unable to play certain positions and forced into them. An option like this would no doubt improve the game significantly and I cannot see a downside from the player's perspective. Please Riot, if you see this, consider it as a viable way to improve solo player queue experience/satisfaction. This could go a lone way to improving the attitudes of players in games simply by allowing them to secure the position they wish to play each and every game.
Also, please up vote and spread the word about this topic to your friends. If enough of the community gets behind an idea like this Riot is sure to listen eventually.
Thanks for reading.