I think some confusion is that the article makes it seem like pageshot.net is separate from the experiment itself. Both the add-on and service are the same experiment, and even hosted out of the same repository: https://github.com/mozilla-services/pageshot/ – you could host your own, but I would actively discourage it now (unless you want to contribute) as we are making a lot of changes and it would be annoying to track.
Another consideration is that we aren't only storing images, we're also storing information about the web pages. For instance, here's the JSON data for a clip of your comment: https://pageshot.net/data/aQOjNCw5wrjvveMC/news.ycombinator.... – of course you can still handle an image plus metadata on the local hard drive but it takes a lot of work if we wanted to support local and remote hosting.
Which leads to the question: why remote hosting at all? A lot of the use cases we see are for sharing. In Mozilla's research we've found that even people's archival habits tend to be built on sharing – people email themselves, send messages to other people for the primary purpose of reminding themselves, etc. My own theory is that to make something useful for your future self you have to go through all the same steps as if you were making it useful for someone else. So you have to pick out something interesting, make sure it is described well, etc. Anyway, we want to support sharing and cloud hosting is the best way to do that.
That said, this is an experiment, and what we're shipping with isn't necessarily what we're going to find, and we're open to suggestions. I'd encourage you to share any thoughts you have here: https://discourse.mozilla-community.org/c/test-pilot/page-sh...
One local hosting idea I've considered is an "all of the above" approach. In that case if you configured a directory to store your shots, then every time you take a shot we'd still upload it, but also same the image (by itself?) in the directory. That would be easy, and maybe it would tell us if this is a valuable direction (and if it was valuable then we might make it fancier than just dumping images). I'd be curious if that feature would make you more open to the concept?