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Currently a player's summoner icon is only ever seen by the people on their friends list and the people they play with in custom games.
With the advent of limited edition or otherwise brag-worthy summoner icons (Pulsefire Ezreal, Season 2 Campionships, Harrowing rewards, Season 2 Ranks, etc.) I think it would be cool to let summoners show off their summoner icons in the champion select screen.
Instead of remaining empty by default, the space where each summoner's champion portrait shows up could show their summoner icon until they select a champion (at which point it would be replaced by the champion portrait).
I think that this change would make summoner icons more meaningful and incentive-ize the collection of limited icons by allowing summoners to show off the icons they have collected to more than just the people on their friends list.
In draft-pick mode the summoner icons of both teams would be visible to all players and would be replaced by each player's selected champion portrait in the normal way.
In blind-pick mode the enemy team's summoner icons would remain visible until the game begins.