In my experience (especially with Elsevier), their copy editors are doing more harm than good. I dread having to go through proofs, as they always manage to sneak in mistakes, from spelling errors to changes in equations or figures.

My advice to students: NEVER just accept the proofs they send you, ALWAYS do meticulous proofreading of the proofs even if your manuscript was flawless. I'm aware of one case where they removed the entire abstract, and since the authors didn't notice that when checking the proofs in the publisher's online proof-checking system, the paper was published that way. They had to publish an erratum with the abstract because, once published, they don't allow changes to articles, even if it was clearly a mistake by the journal. (Disclaimer: It wasn't my paper, so I don't have an axe to grind here; I just found it appalling.)