I've always cut my own hair because I hate salons, but I imagine a successful stylist that comes to your home knows that their clients are looking for personal service and a bit more care & attention than they would normally receive in a salon.
Thats how they get there repeat business.
When you're cutting-in replacement hair, you have to be aware that its important to get it right, because its not going to grow out.
So someone that takes their time and works WITH you is ideal.