I worked in Birkenstock Bostons. Closed toes required.
These days most cities have foot fitting specialty stores and they are worth the cost. The one I go to is a local family-owned store and has a Podiatrist on staff 2d/week who evaluates customers who have foot pain. (She is $25/visit and spent nearly an hour with me). She made me custom orthotics to use in non-Birkenstock shoes to alleviate severe heal pain I had d/t a ruptured Bursa. Those things were a miracle! My everyday closed shoes are Propet.
My sister has been put into Dansko and Keen only. She requires a very high arch as well as footbed support for her chronic plantar fasciitis. With these shoes, she does not need orthotics.
If your foot does not feel supported at every spot, they aren't right for you. So many options out there from flat foot to super high arch, to posterior high arch (my anatomy).