My in-laws are immigrants from Europe, and they have a no-shoe policy. They also have a German Shepherd and a Lab who go out for three walks a day and traipse around in the backyard in between. Makes the lack of shoes seem sort of pointless to me.
I've known people who trained their dogs to stamp/pat their feet on an old folded up towel laid by the door. Seemed pretty ingenious given how wet and slushy the climate is half the year.
For me the shoes thing isn’t about dirt. It’s about public bathrooms. If a shoe has stepped in a public bathroom. Especially those in bars or gas stations I don’t want that shit (literally) being spread al over my house.
My dogs step in their own shit sometimes. They're idiots, but I still generally wouldn't assume a dog hasn't stepped on a surface worse than a public bathroom.
In New York a lot of dogs wear shoes when they’re out in walks, which I assume are taken off when they go back home.