I thought about it too, but I wouldn't know how to do it. And there's legal implications: you'll need to remove illegal images, or copyrighted images.
The way I envisioned such a service is making it completely transparent, so anyone can download a backup of all images. If your service ever disappears, a new one could be started and all that's needed is replacing the links in the forum's database to the new domain name. It would be a way to ensure images are still available in the far future. I started by using tinypic, but they quit years ago so all those images are gone.
The problem with this is the storage of images. Such a backup would take up quite a few gigabytes. But I think the idea is very interesting, and I could think of something.
The service I thought of would use Amazon Cloud hosting or some similar service. To help manage the accommodation. Basically I would only be managing the front end of the site, where the hosting would be provided by these services. Do you think that would be interesting?