The problem with that is people almost never play certain champs in normal (support) where a support is almost always necessary in ranked. And if you've supported with one champion, you can pretty much support with them all, it doesn't take a rocket scientist.
Also, The better players get, the more versatile they become. I know I can pick up most champions and do moderately well with them. For example, I might have played morgana twice in normal, but when we needed someone to play morg just to prevent the other team from getting her, I volunteered, and ended up winning the middle lane (with some help from jungle).
Some people are stuck in this sort of "each individual must be pro at what their doing" and they don't realize that somebody picking morg who would probably feed (without jungle and/or side lane help) or get no cs(not really possible to get low cs with morg), such a pick might actually be the best for the team, even though the morg might be noob.
So no, I don't think there should be any restrictions on the champs you play. Just quit being a ****** and if someone ends up picking someone they don't do well with, just remember that everybody is learning and do your best to help them do better. It's quite possible that the player is specifically countered at champion select, or that all of his or her main champs would have done bad against the selected enemy champ, so they are forced to try something new.