The toothbrush analogy is weird, and untrue in most cases. And regardless, just one time stepping in crap, would make up for a lifetime of a few molecules hitting a brush at random intervals.

And of course, toothpaste is a cleaner, so it's not relevant.

But I find this all amusing, because wherever you take your shoes off? That's where all this supposed crap sits from all these shoes left outside. Which means you are walking in your socks in that area, after shoe removal, and entering the house.

So unless you levitate out of that area, your feet are still covered in this supposed crap.

The shoe rule in Japan stems from damaging floors. And checking your feet, shoes or not, is just prudent. But your feet or clean looking shoes?

Equally dirty.