Well when your doing olys, with the bar moving very fast and with relatively heavy weights, if the grip slips ever so slightly your body shuts down the power. It's not something you notice but it does happen. This also cause you to pull with your arms - ie thick bar cleans and lifts

Plus you can alternate grip olys, or snatch grip deads.
When you hookgrip it, initially it feels like you have less grip, but your used to the sensation you'll find slip is non-existant, and thus you pull harder, and there is less tension in your arms.
No matter how strong your grip is, if you don't hook it, you will have slip and rotation.
Why do you think people lift more with straps?
A hookgrip can actually be stronger than a normal alternate grip when deadlifting. I haven't tested that theory myself, but according to some people who lift some big iron, this is the case for them.