slant 6 head shave

Ok so I am new to this slant 6 forum. I have a new (to me) 67 Barracuda with a stock 225 6-banger. I have heard you can shave the head as much as .060 to give more compression, horsepower and better mileage.

How true is this and is it worth my while? What's the downside to doing this?