I will keep my mortgage forever but not the house. The goal is to carry the mortgage forward to the next house in the most remote and rural location I can find that still has residential fiber.
This is called porting a mortgage, and the lender has to agree to it.
If you have a low-interest mortgage, why would your lender agree to this when you sell your current house and want to port it to another house? I guess there is some incentive, because they will still be getting some interest from you, vs if you pay off the loan, they will get zero future interest. But from my experience with lenders, I doubt they would go for this.
Now sure, if you have a higher interest rate mortgage, they'd be glad to port that in a lower interest rate market. But then that would be dumb for the homeowner.