The posted requirements around footwear in shops/restaurants always seem couched in the guise of sanitation or health codes (By Order of the Health Department). I think this is absurd on several fronts:

• I fail to see anything your bare feet might bring into the restaurant that could not also travel on the bottom of your shoes. If anything, you are more likely to be aware of the the egregious foreign matter (e.g. dog poop) if you were barefoot.
• Sandals and flip-flops seem to satisfy the requirements despite revealing the majority of your bare foot.
• The 'health department' is concerned with food contamination, so it makes no sense that they would be involved with dress codes inside, for example, a bank.

This may very well be about decorum (wanting to cultivate a degree of formality), but then they should just say that instead of pretending it is for health reasons.