There's a fourth scenario - the homeowner pays off the mortgage early. In the US, early payment can involve a penalty, so the homeowner buys out the loan signif

There's a fourth scenario - the homeowner pays off the mortgage early. In the US, early payment can involve a penalty, so the homeowner buys out the loan significantly above market rate. Over the course of a mortgage, a significant number of homeowners will find they "need" to relocate for work or to join a partner or to upsize or downsize. Offering these people a big improvement on "pay a penalty rate to discharge your loan early" would cost the banks money, so they need to pitch any refinancing offer where it makes enough profit off the other homeowners to be worthwhile.