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But there is a notable exception, an use case where a smart contract manages a non-financial asset: Storage management. I refer to systems like Siacoin, where a smart contract checks if certain files are hosted by a server "node" - if yes, it rewars the node owner, and if not, it punishes it. It's possible that there are unknown problems with this approach, but until now it seems to work, while it may be not a complete replacement for traditional hosting, it can be a very cheap, a little bit less reliable alternative.
So decentralized storage systems, even maybe more advanced "decentralized web" concepts (like Maidsafe), could be an interesting non-financial use case. The reason for that is that storage systems have to be reachable permanently by online services, via the Internet - just like blockchains. So the smart contract can directly interact with the service, not with a "representation" of it. No oracle is needed.
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It's a bit nit-picky but I'm not sure if I'd call decentralized storage systems in themselves smart contracts. I'd define a smart contract as a script that is
interpreted by a decentralized network but not
intrinsic to it (eg. storage management is an intrinsic functionality of decentralized storage systems whereas LN is not intrinsic to Bitcoin).
That being said, I fully agree -- decentralized storage systems are a very interesting use case for smart contracts. For example one could imagine a self-scaling system that buys more storage space on the fly whenever needed. Or extending automated web application deployment with a script that autonomously purchases storage space and CPU cycles. Whether such approaches would be viable in practice though are a different question.