You're right of course that with OCR, and the right typefaces, it's always possible to automate the process of building an editable document from a PDF or printed page.
But I doubt anyone would take the hazzle of doing OCR. Because it is still a lot of work to spot misstakes (which still do happen, also with standardfonts).
Also, who would want to lower the perceived visual quality of his resume? And scanning a document, means just that. It will be still readable, yes, but you can see, that it was scanned in.
I suppose you could print out your CV and scan it into a PDF to prevent that - but then there is OCR...