Maybe nobody has spent money to do a study, but it does seem to work. I was skeptical when a friend suggested it, but I'll be darned if it doesn't work.
So it's like Niel Bohr's horseshoe that he hung above his office door. When asked if he thought it brought good luck, he would reply "No. But they say it works even if you don't believe in it."
Perhaps I could kill two birds at once by selling stainless steel horseshoes for bathing use? "Uncle Bohr's Lucky Stainless Steel Bathing Horseshoe" or such?
Luck is hard to measure, smells aren't. I don't understand why you're so hostile to the possibility that stainless steel can remove odors that soap doesn't? This is easy to test. I've tested it.
So you did a controlled test where you used just water one day, a sponge/washcloth another day, and a stone another day and had blinded judges to smell you throughout the day?