Oh, it’s more disgusting than that. You can re-finance which brings your monthly payment lower than what you could possibly afford when buying the same house anew. Yeah, the 30-year horizon for paying off gets reset, but there are ways to work around that.
Back when I was renting the landlord offered a 3-year instead of a 1-year lease. I immediately asked “does that mean I get a discount on rent or lock-in a rate?” When they told me “no”, I asked “why would I do that?” Renters really have no such luxuries.