The house was just a place that was up for rent. Victoria was in charge of rent & had the keys to un-inhabited homes (hence MC buy the key from her & she having a spare to let herself in). The home dosent seem to have much significance in town, it was probably just one of the more expensive (100g up front the weakly) which could be why no one lived there when MC arrived. Also the old mayor was impudent, that was a big part of Victoria's story so I reckon he didnt use it like that...
The mayor does kick MC out to let his son live there (cos hes an ungrateful cunt who decided to kick us out even after all the help we gave- he wasent aware we were banging his wife at the time so that dosent count lol).
After MC becomes Mayor he still owns the house & will use it accordingly. Would be nice to have someone live there at some point tho. I personally wouldn't mind a pet Catgirl to keep MC company whenever he comes home

but that's just me.