You can go further. Invoices often contain block sections of text with important terms of the invoice, such as shipping time information, insurance, warranties, etc. To build something that works universally, you also need very good natural language processing.
This should be obvious, but the answer is because OCR engines are not terribly accurate. If you have a native PDF, you're far better off parsing the PDF then converting to an image and OCRing. But if OCR ever becomes perfect, then sure.
While Abbyy is likely the best, it's also incredibly expensive. Roughly on the order of $0.01/page or maybe at best a tenth of that in high volume.
For comparison, I run a bunch of OCR servers using the open source tesseract library. The machine-time on one of the major cloud providers works out to roughly $0.01 for 100-1000 pages.