Actually, I kind of prefer the stars cut up the way you show in the last picture rather than all exactly the same.
The pulling on the fabric to straighten the grain is the method I was taught back in Home Ec to straighten grain for clothing (back in the late '80s if it makes a difference). I was taught to straighten grain for quilting by lining up salvages and shift until there is no wrinkles and then trim.
For a striped fabric, if I wanted the lines straight then I might try the pulling method and see what happens but I would think that the print wouldn't shift really and would just do what I think of as a more "fussy" cut and just sew carefully to avoid stretching the bias.
I will also admit that I don't know what I would do if I had purchased a kit and there wasn't enough fabric to do the fussy cut I needed to keep me happy. Likely purchase another fabric, and enough of it, to replace the fabric that I didn't end up happy with and just stash the replaced kit fabric for another project along the line.
Tara