@JWChibi
He can't explore the world if he buys a house... unless he can put the house into his inventory. A house in every town? It probably costs a bit more than what he gets for selling materials.
He mentions in ch3 p13 that he won't stay in town for long. With that in mind, he also chooses to avoid getting himself entangled with the local lord and the kingdom, and so took measures such as hiding Feru's identity at first.
What he needed from a town was money for his online shopping. He needs to shop to feed Feru and now, for the goddesses too.
Buying a house in every town would be unfeasible if he were to be traveling. And doesn't he have to pay taxes for it? He has to sell the house once he leaves. If he's gonna do that every time, then an inn would do fine.