Citation, Documentation of Sources

Q. I have a question about citing journal articles that are in print but have only been accessed online, where the online version is a PDF identical to the print version. CMOS states that you need to cite the DOI or URL. What is wrong with citing the page number of the print version as it appears on the PDF, if all things are identical?

A. Nothing.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]