Couple of life long issues here for me.
Not only was I taught that Asians remove their shoes when entering out of respect and to keep from tracking in anything, but because tatami mats (once the primary type of flooring) do not withstand the crushing from shoes well. Can you image what the uprights/stiles of a pair of geta would do to a tatami mat? Bare or stocking feet are far less damaging. From what I have seen in the past 10-20 years, Americans are beginning to realize these benefits and follow suit. They are beginning to notice the divots in hardwood floors that even a slightly built woman in stillettos makes.
But it is still not the general custom in the U.S. To remove your shoes is regarded as beginning to disrobe.
Not something you do just anywhere, especially upon arrival in someone else's house. All my life I was teased that you could "pick out the Texans/Southerners" because we were the ones who removed our shoes at the first chance and usually preferred to be barefoot indoors and out.
When I was a child in England, my nanny's house and part of ours (mostly the kitchen) had bare dirt floors. So the only time we removed our shoes was if they were wet - (1) to dry them by the fire grate and (2) so as not to create mud and track it around. I dare say that if I had removed my shoes, except for bathing or going to bed, my nanny would have been appalled.
As for foot odor, the two primary causes are synthetic materials (hard to avoid these days) and skin problems. As chic as patent leather can be, it doesn't breathe and when you add nylon/spandex in today's hosiery you are doomed to smelly feet. The skin can't breathe, the skin sweats from the lack air and abundance of heat, and the result is unavoidable. At least geta and zori don't have this issue ..... unless the zori are the pretty ones often made of vinyl, or the wood of the geta has been varnished.