I'm glad a podiatrist chimed in. I wish I had a better appreciation for my feet when I started surgical training. I'm a long-time runner with flat feet, but never really had much trouble until residency.
Wore a cheap, light pair of Sketchers when I started residency that really wore down my knees and back after two years. Switched to Sanitas for the last three years and didn't have anymore issues.
However, when I did my CT surgery fellowship, the Sanitas didn't seem to cut it anymore and I got horrible plantar fasciitis when I tried Danskos. It took several months to heal after a podiatrist fitted me with orthotics that I put in a pair of new Asics running shoes, plus compression socks.
If you can't find a pair of comfortable clogs, find a running shoe you like with good cushioning (I agree with the Hokas or Asics), get some custom orthotics from a podiatrist, and wear compression socks. Even if surgery is not your long term career, invest in your feet now if you anticipate working on your feet a lot.