It all has to do with the history of medicine. Similar to DO programs, chiropody was a separate medicine from allopathy. Chiropodist worked on hands and feet, which were commonly ignored by MDs. Podiatry schools started in the early 1900s and have been evolving since. Actually, the podiatry was the only rogue specialty that the AMA supported in the mid 1900s; they were very critical of DO and DC programs, but stated the podiatry was true medicine (probably b/c DPMs implement mainly allopathic techniques). Orthopaedics does have a fellowship in foot and ankle medicine.
Why podiatry still exists is b/c MDs and DOs still don't look at the feet. Most infectious disease and general orthopedist still don't like feet; these would be the specialties that would deal with DM and foot trauma. There has been some criticism in Orthopaedic journals of general orthopaedic training in the foot and ankle and the lack of interest by orthopedist in the foot and ankle.
As for separate education, there will always be talk of integrating the education programs but it would be tough for leaders of podiatric medicine to give up all control (my opinion).
Hope this helps.