Is there some reason I should expect FullSimplify to not use Factor and Together in this expression?
PS: Is there some reason the Sqrt[r0^2] is not simplified to just r0?
I don’t know why FullSimplify does not do Factor and Together. However, you cannot expect it to simplify Sqrt[r0^2] to r0, because it is not correct in general. You can force the simplification either with Simplify[Sqrt[r0^2],r0>=0] or with PowerExpand.