The research is showing more clearly all the time that
Covid-19 is a respiratory virus, in other words, transmitted via particles in the air (breathing it in or possibly rubbing it into your respiratory tract via your eye or nose). Maybe somewhere with a known big load of the virus like an ICU might use clean-room techniques that might include walking through a shallow bath to sanitize the bottom of the shoes, but this kind of thing (and foot washing) have not been a recommended home practice. A lot of people do take off their outdoor footwear when they come home to keep the house cleaner in general, but this generally wouldn't be to prevent Covid.
If you're wearing shoes, what is there to sanitize even if it were possible to get the virus that way, which it doesn't appear to be? If you were walking around in bare feet, it would make more sense, as there's all kinds of stuff you can walk around in, including animal feces etc., but if you're wearing shoes, your skin isn't actually touching anything but your shoe or your socks. But the above is correct, it really doesn't pass by touching stuff, though we wash our hands because of extra caution and because our hands might get very close to our nose and mouth. Not so much with feet.
If the topic of foot hygiene has reached a level that it is actually causing a running argument in your house, I might also add that though the Covid argument doesn't hold water, it isn't unreasonable for one partner to expect the other to have clean feet. The Covid virus won't be tracked in or have fallen on the feet, that's not supported by science. But if someone is tired of looking at someone else's ragged toenails, dirty soles and raspy calluses, well, actually there's nothing unfair about asking a loved one to take care of their craggy feet. Feet should be as well groomed as hands.
If that were really the case it would make sense to throw your clothes in the washer and take a shower after every outside excursion