In principle, the main use case is cloud based algorithm as a service. If google has some service it wants to sell to users but it doesn't want to reveal how it works and the users dont trust google with their private data they can use FHE. The user data is encrypted so google can't extract anything from it to do evil with. The proprietary software stays on google servers so nobody can steal the algorithm. Everyone wins (except of course the progress that would be made if the algorithm was open).
FHE is a really unique primitive, i expect when demos become practical people will come up with new interesting use cases.
There's also some applications to identity-based/attribute-based encryption and multi-party computation, although i doubt that's coming to average consumer any time soon
Well, that's the theory anyway. In practice, researchers say modifying the encrypted memory, then running the program and seeing what happens next reveals something, enough to get them root in fact. [0] But even so, it's a deficiency that can be fixed, so if we aren't there yet we will be one day.
The difference between SEV and FHE is where with SEV you have to trust AMD, but with FHE you don't have to trust Intel. China could have designed and made this FHE chips, and you should be fine. But on the downside FHE is very, very slow (and this won't really close that gap), and expands the data hugely and of course doesn't run conventional software.
To me it looks like that sorts of applications people are discussing here, such as database servers, will be done by SEV because of the shear amount data and processing they have to deal with. The article talks about speeding things up, but the primary bottle neck for those applications is MIPS/Watt. Speeding up FHE by throwing a huge GPU at it doesn't sole the MIPS/Watt problem. However, there are applications that tend to involve primary secrets - things like handling passwords, PIN's, PIN Pads, perhaps even gab.com's OAuth2 bearer tokens that involve tiny amounts of highly sensitive data. Perhaps FHE could be useful in dealing with them.
It lets you do operations on encrypted data. By volume are data centers the average consumer? It seems fairly clear what the benefit would be to them, they can process all kinds of sensitive data that would otherwise be off limits for various reasons.