Why not place the cleats further back on the foot?
First off, i question why anyone thinks the calf muscle is not suited for endurance. Its a very active component of running, biking, jumping and so on. 

The ball of your foot can take hours of running, biking and other activity with high pressure. The arch of your foot is soft, and where tendons stretch across. A cleat in your arch would cause massive pain over time. 

Additionally, the clipped in pedal motion for ideal power is a triangle. Push down, scrape back. This backward pull would be difficult from the arch, and not very fluid feeling. Also likely causing other injuries. 

I am not a doctor, medical professional or trained in physical therapies. Just an avid cyclist that pushes 4500 miles a year, 2 - 3 centuries on a road bike and several other mountain bike events annually.