When does refinancing actually make sense?

Break even, honestly

Divide total closing costs by monthly savings. The result is your break even in months. If you expect to move before that point, the refinance costs you money regardless of how attractive the rate looks.

A no cost refinance is not free either. The costs are covered by a higher rate, which simply moves the expense into the payment. That can be the right choice on a short horizon.

The reset nobody mentions

Refinancing a loan you are eight years into back to a thirty year term lowers the payment partly by starting the amortization over. You may pay more interest across your lifetime even at a lower rate.

Compare against a shorter term, or keep the new term and voluntarily pay the old payment amount. Both preserve the progress you already made.

Good reasons beyond rate

Removing mortgage insurance, converting an adjustable rate to fixed before an adjustment, or consolidating a high rate second lien can all justify a refinance even without a dramatic rate improvement.