IBM Tivoli backup ("ITSM") already exists in much the form you describe. The trick is, I suppose, to introduce a similar product for cheap/free to encourage home users to do it.

Corporate users know how much backups are worth and are willing to pay for the service.

Home users may feel that their data isn't *that* important, or valuable anyway, and will be unwilling to pay money, even to recover it, if the price is too high.

It'd probably be most economical to get an upfront fee, though - otherwise such a service would go through horrendous cash burn up front.