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What are the advantages of a permissioned blockchain over the same collection of entities without the blockchain? If you have a set of trusted entitites that sign and publish the data, why do they need the blockchain part?

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One entity can sign and publish the data, but that doesn’t mean everyone agrees with it. If everyone agrees, they yes they could all sign the data as well. And if the ordering of the data is important, might as well put in a pointer to the previous data. And now we have a blockchain!

You're right, a set of trusted entities don't need a blockchain! It's a terrible datastructure which only makes sense in a very narrow circumstance.

Followed through to its ultimate conclusion, a set of trusted entities should simply run some kind of performant database.

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