If you can deal with the price tag, mainframes are very nice machines in a lot of ways (scalability, availabity, storage). And if you're a large-ish bank or other financial company, chances are the amount of data you need to process and the requirements on availability you need to meet mean you're going to need something mainframe-sized anyway.

Plus, IBM and assorted companies treat backward compatibility religiously, so a random update to the OS or the DBMS breaking your application is pretty much unheard of. That kind of reliability is worth a lot to some companies.

The price tag is rather harsh, though.

Mainframes aren't just about computing power. In a mainframe, almost any component or subsystem can fail with no downtown to the applications at all. That is worth the money and complexity to some people.

You don't understand mainframe systems well if you think they "choke on laughable volumes of documents".

The mainframe isn't the bottleneck in systems like this. It's all the stuff around it that wasn't designed to the same specifications.

Because those simple financial calculations need to be done reliably, for many, many clients at once, without falling over. You can requisition redundant cloud instances equivalent to tens or hundreds of real-world x86 computers, or you can do it on a mainframe. My guess is the cost works out about the same either way.

(Insert image here of IBM System z as Omni-Man, pointing to two fighter jets in the distance marked "AWS" and "Azure" and saying "Look what they need to mimic just a fraction of our power!")

Its not about the complexity of the solution its the scale, mainframes batch processing was the go to solution before the advent of modern hardware. Mainframes were build for resilience but nowadays we have embraced fail early, fail fast to circumvent those scenarios.

Rock-solid reliability for large-scale transaction-heavy workloads.