Now, as for Snort's idea... let me restate it. It involves choosing a role for your champion after you've picked your champion (not while queuing). On the plus side, it does get rid of the queue time problems that exists with picking your role before queuing. Additionally, Snort's idea doesn't limit players to any specific meta, not directly. But here's where I see some major problems.
1) The system is too confusing for new players. When I was new, I only vaguely knew the difference between AD and AP, and only had this general idea of what a tank was from playing MMORPGs (and a tank here is a bit different), I had no clue what terms like "carry," or "support," or "pusher" might mean. The system will unnecessarily complicate the game for newer players.
So you might argue to only implement it for ranked or simply all draft game modes.
2) What problem does this actually solve in ranked/draft? The only problem actually solved is the problem where a player does not communicate how he intends to play their particular champ, and there's a pretty small handful of champs where one can't logically assume how that champ will be played based on the fact that that's the champ.
It won't actually solve issues of "No, I already called mid!" because there's nothing in your idea that prevents someone from calling a role that's already been called. And your idea is for people to choose these cards that indicate role or build type as the champion is selected. The problem with this is in draft mode, the guy who is 5th pick isn't showing his role type until all the other champions have been picked. Moreover, excepting duo queues, 5th pick is the lowest Elo player, so it's actually not in the team's best interest to force him into a role. What if I'm 5th pick and I can play anything but ADC or APC, but I don't get to show cards that suggest this until it's my turn to pick and they've already forced me into a role.
But there are still more problems that are even more similar to the other ideas.
What happens if a new role develops that Riot doesn't have a card for?
What happens if I simply don't select cards when I pick my champion? This is effectively the same as not chatting in champion select. Do I reveal 0 cards? Do I reveal random cards? Am I kicked from the lobby? As it currently stands, I'm not kicked from the lobby for not selected a champion and being random, so it'd certainly be unreasonable if I were kicked from the lobby for selecting a champion but letting the role cards randomize.