It's not a bad look at all. If it reduces Andrew's living expenses, it's a very good look. No-one is being "put out". Harry and his family do not live at Frogmore Cottage: they live in a mansion on the other side of the world. As for his young children, Lilibet has never lived at Frogmore Cottage, and Archie only lived there when he was too young to have any memories of it. They're hardly being thrown out on to the street.
Indeed they're not. They're multi millionaires who can afford accommodation in the London area that most people could only dream about.