The natural followup question is how to make these tools easily trainable for a specific document type.

(After all, a human can do it, with some basic training. Ergo we should aim at computer being able to do it with equally simple training too. And in practice this doesn't seem like an insurmountable goal.)

That's precisely what people do -- they design workflows that leverage AI to handle the forms that it can, and humans to handle the forms that it can't. And constantly retrain the AI based on what the nice humans just labeled. As the AI gets better less needs to go to the humans, but they're always there for the exceptional cases. BTW this isn't theoretical -- this is current best practice.

There are various European standards for embedding XML data into PDFs to make data extraction easier. Think of commercial invoices that need to be both human readable and easily imported into ERP systems.

The French standard is called Factur-X. The German one ZUGFeRD.

More details here:

https://www.pdflib.com/pdf-knowledge-base/zugferd-and-factur...