Isn't there any iPhone app that actually lets you edit the text in a PDF file?

The thing is that all apps I've ever seen let you make annotations only, and not delete one text in order to replace it with another. As powerful as Apple brags itself the CPU in the newest iPhone 6S Plus is (I have that very larger model), isn't there any app that conducts the OCR on a PDF file (or recognizes it in any other way), allowing for actual editing?

A PDF is (should be) a delivery method for a finished document - the equivalent of printing it on paper (which is why generating PDFs is often associated with an application's print options) and as such should not be editable. A PDF can be locked when it is generated to prevent it being edited or even printed on paper. Ideally you would edit the original source document and then generate a fresh PDF version for distribution.

Try…

https://itunes.apple.com/...72073?mt=8

https://itunes.apple.com/...74925?mt=8

https://smilesoftware.com/pdfpen-ios

But just what you can do with them will depend on the nature of the PDF itself.