I'm no pro by any means, but I've worked in a supermarket bakery and a nursing home kitchen back in the day, and I can't for the life of me figure out why clogs are so popular. I don't think an inflexible sole or open back would be comfortable for a long shift, but to each his own. I can only speak for my experiences.
My feet are as flat as a griddle, so I've always had issues with footware. I actually prefer hiking boots (LLBean or Alico) or 8 inch work boots (Herman Survivors) when I'm on my feet for an extended period of time, especially on a non-resilient floor like tile or concrete. Plenty of ankle support, non-slip, good footbeds, and easy to clean. Ecco's and Clarks are a couple of other brands that have worked for me, but I don't know how they will hold up in a wet kitchen environment. None of these are cheap, but I've only got one pair of feet.
FWIW, I tried some Birkies a few years ago and the lasts they are built on just don't fit my feet. Tried on a pair of Mephistos and I have to say they are the most comfortable thing I've ever worn, although they are wicked expensive. Don't know if I'd put in a 8+ hour shift on tile floors wearing them though. I also used to work at WearGuard (now owned by Aramark) and the nurses shoes and postal shoes were very popular with folks who spent the day on their feet.
OnMyWay, I'm with you. Wherever there is a chance of dropping something on my feet, I go for protective footware. Steel toes would be knife proof, but they can be uncomfortable and cold. You might want to look at a polycarbonate toe box. Lighter and more comfortable than steel and they are available with OSHA/ANSI approvals and ratings, just like hard hats and safety glasses. (Not that you need THOSE in a kitchen...)