My Singer 301s are straight stitch only and sew a straight line. The straightest stitching machine I have is 15 clone made for Montgomery Wards - probably from the 50s. I bet my 1949 Necchi is, too, but I have never checked it. I agree that you need a straight stitch machine to get a perfectly straight stitch.
I had a Pfaff that wiggled when I didn't want it too welded. It sews straight now.