Just adding a house will make plot anyway. How do you think Mama will react to message from us that instead of getting us out of here we just stay and let Kokona die ? This is just one line of story, but there can be even more. And how itcan be possibly easie play the game by doing so? You need to spent min 20 gold for a simple house , and by this huge amount of money you could buy EVERYTHIG so it makes no sense even more.
Don't worry about the word house... I have listed the options that can be implemented under this meaning (house - camp - cave - corton box). And the house on this island costs not 20 gold, but much more, “Lona: for 20 gold I can buy a whole house” <- this is a figure of speech to emphasize the high cost of the ticket.
But if you still stick to the word "home". We know that Lona has an identity document. And that in this world without documents you are nothing. Following the logic, for Lona to have a house, she must have documents for this house.
This means that Lona will take over some destroyed hut. And she will put it in order. This place will not become her full-fledged home; she will have no rights to this place. And if Lona foolishly tells Mom about the house, Mom will only laugh. And why should Lona tell mommy about this, they don’t seem to be such good friends. I don't remember Lona telling her mom that she and Kokona spread their legs to earn tickets.
In fact, Mom really doesn't care about Lona, even if Lona lived in the castle, nothing would change. The developer showed this very well.