And where is the money in backing up sites from other hosts? I don't really see it.
Even if for some legal reason the data couldn't be sold it could be offered in exchange for a donation.
This is not "archiving the entire web" it's archiving the type of sites (of size and purpose) that are most likely to need the service.
Best of luck.
You're hoping that somebody 1) has a static website 2) wants to change hosting 3) doesn't have access to the source 4) just happens to call you
That's not a very solid customer.