Why do curlers always spin the stone? Even in case the house is empty and the only goal is to deliver the stone somewhere inside, or when the goal is delivering the stone just to the button and no guard is present (delivery straight by the centerline is possible). In both cases I've ever seen the curlers use a draw.
It is a matter of control over the stone's path.
A rotating stone creates small scratches in the ice with its leading edge, which cause the trailing edge to change direction as it crosses them. This gives the curved path. Explained in this PhysOrg article, which also contains links to other explanations.
Curlers master the skill of judging the rotation and the path of the stone. They have the skill to place the stone where they want it.
If the stone is not rotating, this level of control is lost. The scratches created by the leading edge can cause the stone to deviate to either left or right. The direction of the stone is less predictable. A similar, simpler explanatory article is here.
So, curlers always rotate the stone because that way they have greater certainty as to where it will finish.