My knowledge on it is pretty basic, but as I understand, house spiders are adapted to living indoors: climate, food supply, and so forth. It's probable that over time spiders adapted to live in caves or tree hollows probably found it quite easy to move into dwellings, and stay there, to the extent that now some species have their entire life cycle based around dwellings.

[Edit: I googled around, and this was an interesting article from Rod Crawford, the curator of arachnid collections at the Burke Museum of Natural History & Culture, Seattle talking about house spiders being traced back to Roman times. https://www.burkemuseum.org/collections-and-research/biology... ]

No, they evolved to become synanthropic. That's usually a good deal for a species unless humans change their ways. The black cellar beetle was very popular in Europe living in preindustrial era because it lived in wooden buildings and is now endangered because these buildings are becoming rare.

Generally they can live just fine in the wild somewhere, and human indoor climates merely replicate their natural habitat. Odds are without shelter or clothing or other artificial methods of controlling temperature you'd be pretty screwed wherever you currently live too.