There are a number of complexities involved but external factors outside of system's control are most critical. Consider for example a customer that places an order with a merchant for $800 paying for three items with prices of $200, $300 and $300 - merchant tries to settle $300 for item 2 that is available in the inventory, then $200 followed by $300 the next day. What if the original $300 got declined due to insufficient funds (bank transfers can take hours or even a day to decline)? How does the bank know whether the next $300 is a retry or remainder of the original authorization? The correct operation requires cooperation and idempotent behavior from the merchant, their acquirer, the network used by the customer and correct implementation at the issuing or money holding bank. Implementing distributed transactions and settlement ledgers across multiple parties? That's what blockchains are for but we are quite a ways from that (part game theory, part tragedy of the commons, if you will).

The $300 payment can be modeled as a payment whose state mutated later.

Or it can be modeled as event stream where on {id=2, t=2, +$300} was posted, and {id=2, t=4, -$300} was declined. If you want to distinguish between a "retry" or a "remainder", you add that into the tuple within the event stream.

That is the idea when you control the system. This however is not a system, it is an ecosystem - payments ecosystem. No one party controls the interfaces or implementations between any two counter-parties, let alone multiple counter-parties along the line. The point I was making was infact about lack of control over externalities like this one. For those in payments, this actually is a real problem, especially with small merchants in developing countries but true for even large ones in the west. And this does not even go into the details of cash oriented systems in india, china and elsewhere.