"It is your house. And you are entitled to set house rules. But it is the prime function of the hosts to make their guests feel at ease."
Removing shoes will make some people feel more at ease. They will be able to relax and not worry about dirtying their host's carpet.
If a guest has been informed about the need to remove their shoes, they will be at ease about it. Naturally, we are talking here about unexpected guests. These guests are taking more of a liberty in coming and have to take the situation as they find it. For instance, having come unexpectedly, they may have to wait a few minutes for the host to complete some household task.
I do not think that asking an unexpected guest to remove his or her footwear as he or she arrives (however politely) performs this function. This is an occasion to welcome your guest warmly, and put your customary rules on ice, and your fastidiousness in the cupboard.
Philip Howard sees the shoes-off rules as fastidiousness. I disagree with him. I think it is a lovely and very pleasent custom. Asking a guest to remove shoes is not incompatible with a warm welcome. The guest is being invited to make herself at home and become as the host and family are, shoeless.
"The golden rule of Etiket is to think of others before yourself and your carpet."
I have argued before that having a shoes-off rule is not selfish.