Is it reasonable for an anonymous reviewer to add the completion date to their report to show they completed the review in a timely manner?
Would it be "correct" or "ethical"? Probably.

Would it do anything? Probably not. There are often reasons for a review to come in late, and some of them are not just "The reviewer is a slacker". Beyond that, the editorial staff at a journal has their own discretion beyond just "What do the reviewers say?", and that can (and should) take time.

Assuming you're anonymous, I can't really see an upside as an annoyed author of a delayed paper behind knowing that "It's totally not Reviewer 2's fault".