Consider as an example the following setting.
A set of universities want to keep track of the joint list of students. Ideally, each university will have a "consistent" copy of this list, and whenever some student joins/leaves any of the universities, all the lists get updated accordingly.
Alternatively, we may consider an email service provider that has multiple servers and they want to make sure all servers have the same view of each email account in the service, or an airline wants to make sure all of its servers know in a consistent manner how many tickets they have available. These problems are old, and have had solutions for while.
From my point of view, Blockchain achieved something crucial from a technical (perhaps social?) point of view: consensus in a permissionless setting withstanding byzantine participants. However, there is a huge and old body of research studying more permissioned settings like the ones above, and there are tons of techniques there (PAXOS and derivatives).
My concrete question is: If I have some of the more traditional settings highlighted above, do I benefit in any way from using a Blockchain? (e.g. are they more efficient under some metric? do they scale better to a large number of nodes? are they simpler and easier to implement?). What if the setting is permissioned but we want to withstand byzantine adversaries?
As an interesting note, there might be at least one benefit: you may be able to leverage existing implementations, among which there could be more in the Blockchain domain? But I'm looking for more meaningful benefits.