Is the NA server really small?

I've been thinking about how I'm being paired with anyone from platinum to bronze lately (I'm silver IV myself.) and the auto-fill feature is always forcing players to be support; I couldn't help but wonder... do that many people really even play this game? I know it's a 'world-wide game with over ten million players' but I can't help but wonder how many of those are just bots or smurfs. If there were really that many players, why would my range of ranked players be so erratic? If there were that many players, could you really run out of supports in the lowest of ELOs? Where 70% of the player-base plays?

My only conclusion is that there really aren't that many players, so it has to make teams out of what is available so we really aren't waiting 10mins per game in silver.

What're your thoughts?