Not a manager and not the person you are replying to, but I kind of get their perspective, as I see it somewhat similar to how I treat referral/recommendation letters.
If someone I closely know asks me for a recommendation letter, and they are a person who (in my eyes) deserves a great letter, I just tell them the format for the specific letter (e.g., 2 paragraphs, less than 300 words, what type of content the letter is supposed to contain, etc), and ask them to write it themselves. Then I take it, review to make sure all is good, go over it with the person (in case there are any potential suggestions for improvements [based on my knowledge of them] or parts that i find questionable), edit if necessary with them, and then submit it.
Now that I am looking at it, that's a very similar process to how performance review historically went with my managers.
The manager is also doing you a favor by letting you express yourself to what you believe your strong points during the review cycle were, going over them with you, and helping you come up with ways of writing it that would result in your desired outcome. As opposed to the performance review process (which i've seen before), where the manager takes no input from you, compiles your pull requests/design docs/etc, provides zero context for your work to the higher ups, then "ships it", and you only get to go over the final outcome with them. The latter also counts as "doing your job" just as fine.
What I am trying to say is, just like with referral/recommendation letters, there is a large degree of how much the manager cares about your performance review, how much voice they want to give you in this, how much support and assistance they are willing to provide you, and how much work they decide to put into it on their end.
A wise manager knows that they cannot possibly know your work as well as you do. So they want to work with you on bridging that potential gap between the outer visibility/importance of your work and the true value/effort involved in it.
I really don’t have anything against managers having reports write their reviews. I’m just pointing out there’s a fundamental difference between that and a referral letter, specifically on the “doing your job for you” bit people were talking about.
Saying the manager is also doing you a favor is twisting the words a bit. Sure, you can make the point that it’s nice and it benefits you. But it is a routine part of their current job. Lots of cover letters, maybe most, are being asked outside of this context. Maybe the most obvious difference is it’s within your discretion to decide to not give someone a referral. Not really the same with a performance review.
These differences makes an “okay, but write it yourself” situation fundamentally different.
If someone I closely know asks me for a recommendation letter, and they are a person who (in my eyes) deserves a great letter, I just tell them the format for the specific letter (e.g., 2 paragraphs, less than 300 words, what type of content the letter is supposed to contain, etc), and ask them to write it themselves. Then I take it, review to make sure all is good, go over it with the person (in case there are any potential suggestions for improvements [based on my knowledge of them] or parts that i find questionable), edit if necessary with them, and then submit it.
Now that I am looking at it, that's a very similar process to how performance review historically went with my managers.