So, as dewsanddamps said, there are very possibly changes to the copyedited manuscript, and even if there aren't, someone has to accept or reject all of the copyeditor's changes, and answer all of their questions, for the manuscript to be "final."
Typesetting is much more than copying and pasting into a PDF! Now that we have electronic files, the manuscript no longer needs to be keyboarded, but the text does have to be copied into a design file (typically InDesign) and then all the design choices that have been made need to be applied--how chapter titles are set, headers, etc.
You then have what's called a "galley"--if it hasn't been set in pages. Back in the days of physical typesetting, galleys were long pages just showing the text before it had been pasted into a "mechanical." But I digress. You might also have "page proofs." And yes, those then need to be proofread, to make sure that all of the copyeditor's changes were made, and that all the formatting has been correctly applied, and that no new errors have been introduced.
It's quite a process, and it mostly takes place out of sight.