There are companies, like homeexchange, that have been in businesses for decades doing exactly that. Swapping, vacation rental, subletting have all been around far longer than sites like airbnb. Even craigslist has had a home swapping section for as long as I can remember.

Swapping homes is far more common than renting a room for a week. It's more common outside the US sites like gumtree, leboncoin, etc. have been doing this for years