I would want to amend your question slightly, referring to the house as the only place where Willy can play the role of salesman "successfully." In the house he is free to live in his dream world and does not have to face the harsh facts of his failure in his profession. We are presented with a character who is living in a dream world, a character who makes reality "fit" his warped view of the world and conveniently ignores any evidence that might argue the contrary. Note, for example, Willy's repeated assertion that if his old boss would still be alive, he would be in charge of the New York Sales area - Willy conveniently ignores his age, lack of success and the hardship he has endured in his trade.
It is important to think about the nature of a salesman in relation to this excellent play. A salesman must be able to engage other people and make them believe in what he is saying, and this is something that Willy shows he is able to do - at least in his private life with his family. Consider how he is shown to lie consistently about all the sales that he makes so that he appears to be bringing home a large wage:
I'm telling you, I was sellin' thousands and thousands, but i had to come home.
The trouble was that three of the stores were half closed for inventory in Boston. Otherwise I woulda broke records.
Willy convinces himself so strongly of this truth that he is genuinely surprised when he is forced to confront his financial situation. This is one reality of many that Willy is unable to face.
So, in response to your question, the Loman family home is shown as the place where Willy is most successfully able to be a "successful" salesman, because he is able to create his own form of reality which he imposes on others. It is when the cracks of his alternative world begin to appear that he is unable to face reality, which leads him to commit suicide.