And it's interesting to note that no-one (as far as I'm aware) is doing this. Blockchains have been around for a decade and escrows are still going strong - I don't see any movement to adopt blockchain for this.
For the end user sending a transaction is quicker and cheaper than getting your lawyers to draft contracts, maintaining your own books, paying an accountant or someone else to manage/balance the books, coordinating a deal/terms with them, etc.
Also there's Proof of Stake which is much more efficient than Proof of Work.
The commenter up above is directly referencing where existing 3rd party / escrow services are pretty terrible today and they're certainly not easily accessible to the general public or your average piece of computer code.
A lot of the pre-boom blockchain contract excitement really was as simple as "turn the awful banking middlemen into code so we can get the advantages of them programmatically."
"It's math, bro" isn't actually comforting if the contents of the distributed database are actually in question, perhaps because of mistakes, shenanigans or misbehavior.
No sane risk assessment of "our company depends on this being correct and consistent" is going to sign up for this.
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 the 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?