Running from old-fashioned, centralized data centers would be dangerous in case Austria (or any other country) gets nuked off the map because then the data centers would be gone. So I guess you meant centralized in the sense of ownership, not location.
An advantage e.g. is the dynamic management of assets. Right now this stuff must be notarized — ever single change. When using a smart contract you only need to notarize the smart contract and then the spouses are free to add and remove assets as they wish. Everything is transparent, no third party has access and in case of a divorce everyone can see the latest state and how it was created.
As you already stated it’s also possible to tell whether someone is married or not if there is any kind of marriage register on the blockchain in the future. And this would yield definite benefits if this is shared across countries.