Presentation app is on the roadmap. Honestly, I've been waiting to see how much demand there was before we launch into that.
And yes, you can host since this is a serverless app. If you go to the repository, you can clone and run locally or deploy to the domain of your choosing if you want.
The key thing to note, though, is that the app origin is used for storage. So, if you create documents locally, they will be accessible anytime you run the app at localhost:8080 (or whatever port), but they won't be accessible at app.graphitedocs.com. Similarly, if you self-host, those documents will be available at that app origin domain, but not others.
If you want to use Graphite and share files, the best bet is to run it at app.graphitedocs.com, but you absolutely do not have to.
For a full replacement I would require a presentation app though.
Is there a planned option to selfhost the frontend for personal (and/or limited) usage?