Starters and relievers

I was wondering why baseball teams don't use 11 relievers to pitch 2 innings at a time instead of the typical mix of starters, relievers, and closers. Relievers are cheaper than starters and typically have lower ERAs for the innings they pitch. Last night, I heard some compelling reasons why this probably hasn't been tried by Billy Beane.

1. Relievers throw fewer innings overall during the season (likely ~60 vs ~200 for starters). If you were to have them throw more innings, they would have higher ERAs.
2. Relievers typically throw two or three different types of pitches well, while starters can often throw four or five. This would make hitting easier for batters.
3. It would be hard to find enough starters who are transitioning to being relievers to execute this strategy effectively.