File-sharing is more of a usability problem. Invention of email + attachments solved file sharing a long time ago. Its the integration with your everyday life that has been a challenge up till now and this is what Dropbox and iCloud are solving.
Companies like YouSendIt never became as successful as Dropbox because they were before their time; and when the time came, they failed to innovate instead hoping for people to adapt as they adopt. Except I don't think they did it right.
You don't want to pay for file sharing as a feature; but it'll be part of the infrastructure that runs your life. Its synonymous to when Bill Gates' separated the software and hardware and focused on software. No customer wanted to pay for it; but the companies that made the hardware (IBM, Apple) did want to pay for it.
What does it mean to "solving a problem"?? Every attempt at a startup has and solves some kind of problem.