I suppose you could force yourself to take the club straight back and straight forward if you really wanted to and didn't care how akward it feels?
Personally, I think it is better to use the stroke that comes most natural to you and that you can repeat consistently.
Consistency is actually the point in putting: if you can become consistent with your stroke, you can also teach yourself to hit the ball where and the distance you want it to go.
Once you learnt that you still need to learn to read the greens so you know where you want it to go.
BTW, I open and close the face when I putt.