The reason so much time is spent negotiating legal agreements is to reduce the surface area of dispute. On one hand, we want to reduce the possibility of misunderstandings that could lead to a "shooting war" as you put it, and also to reduce as much as possible the scope of the matter that may need to be evaluated by a court in the event of a litigation.
Using a blockchain in a situation like this can make achieving both of those objectives much easier and less costly from both legal and operating points of view. There would still need to be some contractual relationship among the participants, but the scope of the contract can be simplified and reduced.
And if the number of participants involved exceeds two entities, a blockchain can vastly simplify the relationships of all the participants with each other, without needing to empower a centralized entity to coordinate among all the participants.
> Human history has lots of "people don't trust each other" scenarios, and they've been resolved in the past, with reasonable efficiency, without blockchain.
Sure, but what's wrong with reducing costs and complexity even further?