Exactly. But we have no real coordination or uniform application in how we're creating PDFs across all these programs so we always end up with a fun mix of what will and wont be static, scalable, searchable

Exactly. It’s pretty insane that we have converged on storing documents as PDF. And it looks like no work is done on making PDF files machine readable.

Yes this is already possible. You can look up the ZUGFeRD standard for an example of how this is done for German invoices.

See also:

https://pdfa.org/resource/pdf-2-0-application-note-002-assoc...