On the bass and cello (and probably violin and viola as well), it seems like many aspects of proper form serve the purpose of getting ones arm over the left shoulder to play high on the fingerboard. So, are there any instruments that have been built with the left shoulder made concave?

If there haven't, is it just a chance thing that no one has thought of it or felt the need for it, or are there acoustic reasons to keep the instrument roughly symmetrical?