In the UK, where the BBC is hosted, solar-powered headphones are mostly a waste of time. It rains a lot and you spend a lot of time avoiding being outside. Most people are at work when the sun is highest in the sky. As others point out, most people can get through the whole day on one charge.

It would be much more efficient to put solar-panels where they can maximize their potential energy output and instead just charge normal headphones from renewable sources. Bare in mind that the creation of the solar panels themselves has a carbon offset that the application of headphones is unlikely to recoup.