Not necessarily. At least in the US, you can refinance to a lower rate when interest rates decline. Sometimes you can even renegotiate the rate of your current loan with your lender because they'd rather you pay them less than have you refinance with a different lender so they get nothing.

You can also sell the house and move to a different one. In the US, the average time people stay in a home they bought (with a mortgage in almost all cases) is between 10 and 13 years.

Renting is great in some situations, especially if you can't afford a mortgage, or find the flexibility of being able to move elsewhere in a year (and don't mind often being forced to move), or you find taking on a 6-to-7-figure debt too uncomfortable psychologically.

However, in most cases buying a home, even with a mortgage, is the more financially savvy move.