I ran some quick numbers and $2000 seems to be about what you would need to keep an average website (www.aaronsw.com for example) and its contents up forever assuming base needs and bulk registration renewals.
Would anyone pay this?
The sites would need to be static snapshots and piggy back off the main domain. You could direct traffic from external domains, but those domains would likely die at some point. Perhaps you could even partner with a DNS service such as CloudFlare so that users could have an option to direct traffic to your service when certain actions happen (site is down for a certain amount of time.) The domain would still die eventually though, and the links would go with it. Ultimately I'm not sure that losing links would be a big deal anyways, as links to your main domain would die off eventually as well.
This service would be sort of like a love child of Tor and archive.org except that it would specifically be setup so that your site would always have a URL to reach the site directly rather than having to do a search. Archive.org might already have a scheme where links to a site snapshot will never change, but I'm not sure about that as it's probably not the main focus of the service.
I think this would be more interesting that attempting to build a commercial service. A commercial service would probably end up being like a ponzi scheme where you would need enough new users to cover costs to pay for the old users. Archive.org and Wikipedia seem to be doing okay though, so perhaps you could go the same route as a non profit but on more typical hosting infrastructure.