Pick/Ban Questions

I'm sure this has been talked about before. I was just wondering why the first three people to pick aren't the ones who get to ban? the only pro to picking first is that you are almost guaranteed the champ you want, but you have no chance to counter pick, so you're kind of forced to pick someone safe that you may or may not want to play, or pick your main. So why not let people pick who they want to play and be able to ban a hard counter, and then let the people picking last be able to counter pick? I might be like totally wrong about this but I've always kind of wondered why...

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