Our Sun is 4.6 billion years old. It will burn about another 5 billion years or so. It burns hotter now than it did 4.6 billion years ago because stars burn hotter the older they get for the reasons you explained. Starlifting is a fountain of youth for stars. We'd want to engage in starlifting so our sun doesn't roast us in another billion years and provides utility to the earth and its inhabitants for trillion of years. The metals obtained in the process are just handy by-products.