IMO, whether or not you can draft a LOR for your recommender is a controversial subject among adcoms and not something as cut and dry as some people might suggest. On a continuum, it is clearly wrong for you to sign the writer's name to a letter that you wrote and send it off yourself. It is clearly wrong to demand that the writer give you a copy of the letter if you have signed the waiver and given up your rights to see it. (However, the recommender *may* voluntarily choose to give you a copy without you asking for it.) On the other end of the spectrum, it is clearly ok (and even beneficial) for you to tell your recommender what topics you need covered in the letter and/or to give them a copy of your PS. This will help them write a better letter.
Drafting the letter yourself falls somewhere in between. It clearly goes a step farther than just providing the recommender with info; you are actually having perhaps significant input into what the letter will say. There is a chance that the writer will be "lazy" and just sign off without substantively evaluating what you've written. If that happens, then of course the LOR is useless to the adcom. On the other hand, no one else knows you as well as you know yourself, and no one else cares nearly as much as you do about getting a strong LOR completed in a timely manner. If the writer asks you to draft the letter and reserves the right to edit it later as s/he sees fit, you could argue that this is not so different than you telling the writer what you need them to write about and them physically writing down and using your words.
What I'm getting at here is that you have an idealistic side arguing that the student should not be involved in writing the letter at all, no matter how much it inconveniences either the student or the letter writer. Not involving the student is obviously the best scenario for all involved, as it avoids putting the student into an awkward situation. On the other hand, there is the pragmatic reality that sometimes, if you want the letter to get done, you need to be more proactive about it than nagging your writer every week or two, even though having students drafting LORs is not the way things are supposed to run. There's no question that this does put the student in an awkward position, especially given the power differential between you and the letter writer.
As I said, I don't think there is a clear-cut right answer about whether to draft the LOR at the writer's request. Each of you will need to decide for yourself how comfortable you are with doing this.
