I had a couple of pairs of shorts that came with a drawstring. I pulled the drawstring out. It's not necessary.

But anyway. Regarding the OP, if you wear unpadded tights under bike shorts, you'll probably wind up with seams in painful places. To me, preventing pain is more important than the way tights-over-shorts looks.

Chamois tights under chamois shorts would also be painful. Too much bunching of fabric and padding would lead to chafing.