I think a big reason for this is that PDF editing tools are just pretty terrible.

PDFs are meant to be a presentation document format, not an editable document format. I have some experience editing PDFs, and it's difficult to make significant modifications. Editing small sections of text or replacing a date is fine, but once you try to start editing entire paragraphs or changing the layout, it quickly becomes unmanageable. The kerning looks weird, the spacing between words looks off, and when you look into it you realize the the sentence you're trying to edit is actually split across a dozen text objects. For these it becomes almost impossible to edit without destroying the spacing, so you just give up.

And the approved way to edit these PDFs is via Adobe Acrobat Pro, which costs $20/month (ugh), which I'm not willing to pay for.

So I think this is why we just don't see that many PDF forgeries. The editing tools just aren't very good. Maybe it's different now we can just ask Claude to edit our PDFs for us.