What is a relatively young band like Rage Against the Machine to do when their singer quits? Imagine the frustration. You spend a decade building this band into this massive entity, and then one guy bails and you're screwed. Rage weren't ready to throw in the towel, so they picked up one of the biggest free agents in rock and carried on. Wisely, they changed the name. Unwisely, they picked the uber-generic Audioslave. Early tours featured nothing but Audioslave songs, but they eventually folded and brought in Rage and Soundgarden material.
Chris Cornell is an amazing singer, but watching him sing "Killing in the Name" was a pretty gnarly sight. It wasn't totally his fault. Zack De La Rocha is the only man on the planet who can pull that tune off, and in 2007 he returned to Rage and the whole world forgot that Audioslave existed. Unfortunately for all parties, YouTube exists, and footage of Chris Cornell signing "Testify" will never go away.