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DELETE FROM … RETURNING
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You are correct about UPDATEs needing to be passable as they are updated - i.e. there is no way to defer constraint checking till the end of a transaction, so every record update needs to succeed as if it was the only update in the query, yet also not rely on the full completed state of the transaction to check its immediate constraints.   
That also means that your update order within a single statement, if it was possible, will still not solve this problem.

I think the people who advocate for this are maybe more concerned with triggers and FK actions happening in predetermined order on UPDATE and DELETE, but for that it's best to rely only on yourself and post those transactions/queries in the exact order you want them executed. No engine quirk or different DB engine's habit can ever mess with it then.