There are some who think that asking guests to remove their shoes is contrary to the principle of hospitality.
This is a culturally relative matter. Albania and Turkey are countries in which hospitality is greatly valued and yet it is expected in those countries that guests remove their shoes.
The shoes-on people argue that a hostess should primarily be concerned with her guests comfort and not with the state of her carpet or floor. However, most guests will feel more comfortable after removing their shoes. They may, admittedly, be uncomfortable because they are embarassed about their feet or they feel their shoes are part of their outfit. Those problems can be dealt with by letting guests know in advance that shoes-off is expected and so they can either bring slippers or plan their outfits with bare or stocking feet in mind. Any embarassment should be minimal if guests are not taken by surprise.
In my opinion, those who insist that guests should be allowed to keep their shoes on take hospitality for granted.
When I get my own house or apartment, I may well invite you. I will give you the best seat. I will cook for you. I will serve you the best food I can. I will give you whatever you want to drink, whether it be alcoholic or not. I will give you my undivided attention. I will entertain you with conversation. If you live nearby, I will drive you home in my car. If not, I will let you stay the night. I will wash up the dishes and cutelry you have used and clean up any mess you make. Given that I am willing to do all this for you, do you really think it is so unreasonable that I ask you to take your shoes off?