No, you actually step out of your shoes an up to a wooden platform which shoes never trod. And yes, the top and even many middle level dining establishments in Japan actually do require guests to leave their street shoes in an entry way, called a Genkan.

Nobody steps with their socks onto shoe trodden surface. It's not a complicated but of geometry, you loosen your foot in the shoes to make them ready for stepping out from, then step up onto a raised and dirt free platform, then if you have good manners, turn around, lower yourself, and use one hand to collect and turn your shoes so that they are not in the direct line of traffic and are facing away from the house, so that one may step into them from the wooden platform without needing to step backwards as you exit. This is amazingly simple, done by literally millions of people every single day, multiple times, and has been this way for centuries in all kinds of weather and many styles of shoes.

There is no dirt tracked in on your socks, there may be some 'stepping on the top of your own shoes' if you are in a rush and clumsy or a child. But grown ups rarely have much difficulty with this unless they are visiting from somewhere else and cannot be observant. Nearly every doorway in the country also has a handy long handled shoehorn to ease the donning of your shoes without requiring a seat. Community centers and elderly homes and some households with elderly residents will also have a small stool that is at an oblique angle between the 'dirty' shoe level and the clean wooden platform, allowing one to sit and take off shoes, then swivel without putting feet onto filth and stand again in the clean.

I'm frankly astonished at the seemingly purposeful denseness of comprehension for a simple act of cleanliness. The 'filth will make us stronger' approach reminds me of the historical writings of the 10th-century Arab diplomat Ahmad ibn Fadlan, who chronicled the Volga Vikings (Rus') and was the inspiration for the 'Viking morning bowl' scene from the movie The 13th Warrior. Just 'Ewww'