re: Why do they keep racing American Pharoah?

There's plenty left for him to do on the track. He may have won a bunch of grade 1 races, but he has yet to run in a non restricted stake.

Don't worry, they are playing it safe. He'll stay age restricted til the classic,

And as far as a broken leg goes, would you like me to list all the nice stallions we lost to paddock accidents just this past year? Because horses don't only break things in races. Some even die while breeding.