It's been 35 years now, but IIRC I had an undergrad professor who had me write my own recommendation. If my hazy memory is correct, I think the way he handled it was perfectly reasonable. I gave him the letter, and we may have gone through one or two drafts after that. Most likely it was much more time-consuming for him than if he had just written the letter himself. I think the idea was that if I had taken a freshman class from him, and he was writing a letter for me three years later, it would be very unlikely that he could remember enough to say much more than, "Good student, got an A in my class." Having me at least write the first draft would mean getting some more about me as an individual. I don't think there was any tendency for it to be inflated compared to a letter he would have written on his own. If anything, I think I was hesitant to overstate my own case.
These days if I have a really strong student, and I want to go the extra mile to write them the best possible letter, I usually ask them to provide me with lots of written materials to fill in my knowledge about their life. I have them send me their statement of purpose or admissions essay, and I try to draw them out by email or in person about their life, or things they did in my class that I had forgotten. In many cases I don't know until this point that they were in the military, or were the first in their family to go to college, or had had to overcome an invisible neurological disability. I doubt that the result of this process is much different than the hypothetical result I would have obtained by having them write a first draft of the letter.
I teach physics at a community college, and many of my students are poor writers, so letting the student literally write their own letter without revising it afterward would be a disaster. It would be an ineffective letter, and it would also make me look like I didn't know how to write. For the same reasons, if I have a student I really think is great, I will ask them to let me make comments on their statement of purpose or admissions essay before they send it out. Often what they give me is just abysmal, and they have no clue that it's bad. Many of our students are not native English speakers, or have grown up in households with no books. Their humanities instructors don't seem to require them to do much writing, and if they do require them to write, the standards seem to be incredibly low.