You could do the work and allow them to supplement what you've noted down.
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.
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.
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.
I do believe them doing the work is important to point 1., putting them in-control. The most important part of my job is setting them up to succeed. If they require their manager to always positively advocate for them, they are leaving their careers up to change. Not all managers are looking out for their directs, so teaching people to look out for themselves is important to me.
Your job is to know how the team functions together. What are the skills of your team, who is better at what, who gets on with who, etc. You going to ask them each to write that down too?
I get the value of having them also do it for themselves, but if they write down total bullshit are you going to spot it? Seen that happen. Or if they miss things that you thought were valuable and they didn't? Are you planning on just remembering it six months later?
>I am a lazy manager
You will do well in corporate America or higher education, apparently.
While I joke about being a lazy manager, I do not agree I am uninformed.
I have ~20 hours of 1:1s per week. I take detailed notes of every single one (transparently, as I share my notes with the person I am doing 1:1's with).
Because I am talking with everyone across the org, constantly, I am getting a constant stream of data on accomplishments, struggles, motivations, working relationships, and performance. I can instantly name my top and bottom performers, by level, and go into detail on why they have that rating.
The accomplishment tracking that I have engineers do is more of an internal resume. It could even prove to be an external resume.