One reasonable way to keep detailed records of transactions is a blockchain!

The best thing about a blockchain in a situation like this is that the different participants don't need to reconcile their transaction records to make sure they agree. Reconciliation—which is costly and can lead to disputes—is unnecessary.

Of course there are other technologies you can use as well, but using a blockchain would be easier and cheaper—especially if additional parties begin to participate in the arrangement as well.

It's not reasonable, because the moment you have to interact with things off the blockchain, like dollars or physical stuff, you get the same reconciliation problems you had before. It's needlessly complicated for no gain.

Reconciling digital records against physical assets is something that all electronic systems must contend with. But traditional multi-party systems also need to worry about reconciling each entity's records against all the other entities' records.

The blockchain simplifies the arrangement. Where is the additional complexity you are referring to?

The use of a blockchain itself is the complexity, and it is a tremendous amount of complexity. All the smart contracts, infrastructure, and cryptography that it entails adds up. And there's the maintenance burden of setting up and running a byzantine fault tolerant system - If this is a private chain, who owns the servers and how many votes for each participant? How do you keep the voting fair if one side has to scale up more than the other? If this is a public chain, how do you keep your transactions private? What if there's a bug in the chain or the smart contract?

All of these questions need serious consideration if you are doing real business. Particularly when a database looks like it gets you 98% of the way there and your legal department covers the other 2%. What value is a blockchain actually adding compared to MySQL and a lawyer?

After all, the threat of a lawsuit is enough to keep the databases in sync almost 100% of the time, and to resolve most other problems quickly. For anything more serious, you will need to do a full reconciliation of the stuff and the money, which a blockchain won't help you with anyway.