It's not just about outsourcing compute. There's lots of interesting things you can build on top of an FHE primitive. The linked blog post has the private information retrieval example (the database owner doesn't want to send you the whole database, you don't want the database owner to know what you're looking for). I have a worked example for machine learning here: https://juliacomputing.com/blog/2019/11/22/encrypted-machine... (The model owner doesn't want to share the model, you don't want to share the image you're asking them to process).
Was just about to post this here if no one else had yet. Really cool stuff! This was the first example I saw of FHE where I was actually able to easily run the underlying demo code [1] on my own system.
