You probably could have come up with this answer yourself, but going this route saves one the cost of a new frame. In the US, at least, there’s no separately itemized charge for installing new lenses in a frame provided by the customer.
The key is that the optician/optometrist will most likely need to send the old frame to the company that grinds the lenses to make certain they fit properly, so this option may not be available for frames currently in use.