A bit late, but I can answer your question. The reason that every accounting solution is unique is because every company is unique. Your accounts represent different aspects of your business. You need to track all of your assets, liabilities, inflows, outflows, etc, etc, and what these are in particular, depend very much on the particulars of your business. If you're heavily leveraged, your reporting requirements will be different than if you're self funded and that affects what accounts you may or may not need. If you extend your business into a new market, you may or may not have to set up new accounts to deal with local laws. Add a new location and that may or may not require changing your accounting structure depending on your requirements. Create a new subsidiary as an LLC, and now you have a lot more work to do. If you have the same teams working contracts for multiple lines of business, that's another layer of complexity. In other words, your accounting practices reflect the structure and style of your company.
For a more concrete example, I'll tell you about something I have some experience with, commission systems. Commissions seems like it would be something that was straightforward to calculate but it's tied to business strategy and that's different for every company. Most companies for example will want to compute commissions on posted invoices, which makes the process much simpler because posted invoices are immutable, but I once built a commission calculator for a company years ago that often had a long gap (months) between a booking and when they could invoice the client, so they wanted to calculate commissions from bookings but only pay them when invoiced. Because bookings were mutable, and there were legitimate reasons to change a booking before you invoiced it, that, combined with a lot of fiddly rules about which products were compensated at which rates and when, meant that there was a lot of "churn" in the compensation numbers for sales reps from day to day; they're actual payment might differ from what they thought they earned. That was a problem that the company dealt with, the tradeoff being that they could show earnings numbers to the sales reps much more quickly and incentivize them to follow up with the clients on projects so that they could eventually be paid.
I remember another commissions situation where there was a company that sold a lot projects with labor involved. They were able to track the amount of labor done per project, but they compensated the sales reps by line item in the invoices, and the projects didn't necessarily map to the line items. This meant that even though the commissions were supposed be computed from the GP, there wasn't necessarily a way to calculate the labor cost in a way that usable for commissions so the company had to resort to a flat estimate. This was a problem because the actual profitability of a project didn't necessarily factor into the reps' compensation. Different companies that had a different business model, different strategy, or just different overall approach would not have had this problem, but they might have had other problems to deal with created by their different strategies. This company could have solved this problem, but they would have had to renegotiate comp plans with their sales reps.
There are off the shelf tools available for automatically calculating commissions, but even the most opinionated of them are essentially glorified scripting platforms that let you specify a formula to calculate a commission, and they don't all have the flexibility that manager might want if they wanted to changed their compensation strategy. And this is only one tiny corner of accounting practice.
Basically, when it comes to arithmetic very few accountants are out there manually summing up credits and debits. In large companies, the arithmetic has been automated since the 70s; that's largely what those old mainframes are still doing. But every company has a different compensation plan, different org structure, different product, different supply chain, different legal status, different reporting requirements, etc, etc, and that requires things to be done differently.
> What information do they use to validate numbers? Why is it not possible for today's AI to do it?
For an example, they would need to cross check with a sales rep and an engineer to makes sure that the engineer had not turned on a service for the customer that the sales rep had not sold. If that happened, they would have to figure out how to account for the cost. Given that the SOPs were written in plain English, I suppose it's possible that an AI might be trained to notice the discrepancy, but if you could do that, you could just as easily replace the engineer. And that didn't account for situations where the engineer might have had an excuse or good reason for deviating from the SOP that would only come to light by actually talking to them.