Know of Bill Folberth? If not, you should.
In 1933 William M. Folberth and his brother, Frederick G. Folberth invented and patented the center shot bow. They also were responsible for vacuum operated windshield wipers in 1921, an improved rear view mirror in 1928, a respirator that fit over your nose in 1951 and a couple of other automotive items.
Bill Folberth was an accomplished bow builder also. His bows had an unusual limb shape.
In 1939 Bill Folberth built a center shot bow. He found that, if shooting with fingers, right-handers shot to the right and left-handers shot to the left. If they used a pinch draw or Asiatic style draw that problem was alleviated, (see text). It was concluded that this style of bow was not better than conventional designs and perhaps not as good. This was by no means the first and only attempt at a shoot through bow. SABO had the SSR recurve in 1969 and York Archery Had shoot through compound bows in the 1980's. Many current compounds use this design and Ambush Archery and Petron Archery make recurves.
Bottom photo of bill Folberth shooting a bow of his design.