You know what can easly solve that? Achievements
Things like "most magic damage dealt", "most physical damage dealt", "most physical damage absorbed", "most magical damage absorbed", "most healing done on an ally", "most times CCed an enemy", "most wards used" and so forth
True, we do have (most) of these statistics in our match history, but it could be fun to actually win something based on certain milestones (even if they don't appear during the game, only after the match). Specially if it's ranked on bronze, silver, gold, platinun etc...
Who knows? Maybe then people will actually want to tank, support and do other valuable stuff during the game besides trying to kill everyone (and dying in the process)