This is a good idea in theory, but not if in form of a company. This would require something like a consortium where Google, Microsoft, Twitter, Facebook, ... and a few more federates to create a service paying for the bill and with the intention to take it up for the future as long as possible.
Plus there's already a service that does the same thing, is free, and is heavily relied upon, WebCite.
There's also the DOI system that mostly solves this problem for more permanent material ( research articles).