So you have flat feet and the podiatrist recommends supporting them which further increases your reliance on support?
The people recomending barefoot or low drop, wide toe box shoes definitely have something.
The more you support your feet and ankles, the more they rely on that and therefore the weaker they get. Using the muscles in your feet and getting them to support themselves seems like the best way to sort this out. As OnzaDog also suggests.
Spend more time barefoot, get zero drop shoes with wide toe boxes: Altra, Vivo, Lems, innov8 have a few, Merrell barefoot range, Xero, Vibram FF.