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? As a referee, I like to submit my reports in a timely fashion in order to avoid unnecessary delays in the publication (and also because I hate when referees spend months and months reviewing my papers). However, I have noticed that sometimes the journal does not make a decision on the paper until several months or weeks later. I have an example when I submitted my report in July and the decision was made in November. I was wondering if it would be correct/ethical to put the date on my report in order to show the authors that my report was submitted on time, even if I am an anonymous referee, and that other referees or the editors are to blame for any delays.
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".