There are a few services like this today, some are fairly simple like memorial web pages or find-a-grave where you can add photos about the people named on the tombstones.
Expanding beyond that (and I think more useful) are eternal digital archives such as https://www.permanent.org/ which is a non-profit that charges you per gigabyte for perpetual storage. They store copies of your data with multiple providers (AWS and Backblaze right now) and promise to transcode formats as technologies change. you can make the archives public (letting you have the "eternal home page") or private so only certain people can view or update it. The money you pay goes into an endowment and the earnings from the endowment pay the storage costs.