It's a good idea in theory, but in practice, it's not so simple. It would be one thing to say "everyone has to play all the roles when they first start playing, so they can learn them all." But let's be realistic. Most people have absolutely no idea what they are doing when they first start playing, and if you take into account how awkward it can be to learn how to jungle, or laning against smurfs, it can be a very frustrating thing to make people constantly switch roles up just when they start to get comfortable in one. But, if you wait until they have more of a grasp of how the game works before tossing them into a new role, they still run the risk of coming up against an enemy who is much more confident in that role than they are. (Which can honestly happen even in roles that someone mains.) So, if they try to learn the new roles, they get flamed by their team if they do badly. (Because everyone is a diamond smurf xD )
I think if there was a way to work it into the beginning learning process it would be a good thing.