This sounds like a missuse of teachers time and a waste of money. Any person who works with the kids, teacher, teaching assistant, even dinner lady can soon see what kind of background the child comes from. The childs dress is the most obvious, is the child clean, can they eat properly with knife and fork etc etc. Also the way a child speaks is an indication of upbringing. All this can be observed without sending a teacher to the home. My daughter who is educated well above that of a normal teacher would be horrified at the thought of a teacher visiting and would spend days cleaning and tidying the house, as would most parents. The visiting teacher would see an artificial environment.
My DGD can eat with a knife and fork (after a fashion), says please when requesting a treat, and thank you. She is well behaved when visiting a restaurant and is bright and articulate and she under 2. By the time she goes to school, hopefully she will adapt well and settle.
By contrast some kids I see swear, and are bad mannered and have knowledge of how to behave in a civilised manner, these are the ones to have an inspection visit.