It's a house, not a museum
Ever heard that before? On internet discussions about shoes-off rules, somebody on the shoes-on side usually makes this comment.
Logically one would think that this entails that removing shoes in a museum is normal, while removing shoes in an house is not. Have the people making this comment ever been required to remove their shoes in a museum? I have. It was in a museum devoted to Sumo Wrestling in Japan. In a country where removing shoes in public buildings is common, like Japan, one will find museums with a shoes-off rule. You might perhaps find them in a country with harsh winters, like Canada or Norway. However, you would have to search hard to find such a museum in the UK or the USA.
There are some very significant differences between museums and houses. A museum is likely to get a constant stream of foot traffic from visitors. Hence, contrary to the statement above, one would actually expect a carpet in a museum to be a lot dirtier than a carpet in an house.
You are not very likely to sit down on the floor of a museum. Nor are your children likely to spend much time playing on the floor of a museum, or at least you would prefer they did not. You won't be eating in a museum. You won't be walking barefoot on the floor of a museum, unless it is one of those rare museums we mentioned with a no-shoes rule.
A museum is also likely to have a dedicated team of cleaners working there every day. You might be fortunate enough to be able to afford one cleaner to visit your house once a week. but this is too expensive for many families.
Having a shoes-off rule in a museum might not be a bad idea, but you have a lot more reasons for wanting shoes-off in your house.