SQLite is a tricky beast. It's great if you're working single-threaded, but a Terrible Idea if you've got more than one concurrent connection. You use it because it's easy to setup, light, and portable (it's just a file).
In Paperless, we've built a self-hosted web application, so it makes sense to standardise on something small & light, and as we don't have to worry about multiple connections (it's just you using the app), it's a perfect fit.
For users wanting to scale Paperless up to a multi-user environment though, we do provide the hooks to switch to PostgreSQL .