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What is the incentive for a bank to refinance a mortgage at a lower rate?
The reason is the same as with cell phones payment plans. As competition grows cell phone companies offer better payment plans for the same price or the same plans for lower price or both so that you stay with that cell operator. Banks also make better offers if the financial situation allows. Suppose several banks offer refinancing with better terms but prohibit refinancing loans from the same bank. Okay, you refinance from another bank and them maybe refinance the new loan again from the original bank - it's a new loan after the first refinance and prohibition no longer works. They just make you jump through more loops and it doesn't make sense neither for them nor for you