You asked about sandbox compared to "using the normal draft mechanism". I hope I understand correctly that by this you mean that you mean feature of Stack Exchange software that if you start to write a question (or an answer) and you not submit it, you can find it in the same place again later. (This feature was announced here: Allow questions to be saved as drafts prior to posting. It is listed as 2010-10-01 in Recent feature changes to Stack Exchange.)
Some aspects of drafts on this site that can be considered disadvantages:
- Drafts on the site are kept only for a limited time. (The announcement linked above says 7 days. Somebody might want to come back to the same post for a longer time.)
- Drafts are not completely reliable. (Many users have mentioned that they lost their posts in this way.)
- Draft is only visible to you, so it does not help if you wish to ask somebody for their input on a post you have prepared (but haven't yet posted).
As another option you suggested to make a post here on the site, delete it and edit that. Again, there are some limitations, but it is doable.
- As you cannot edit a self-deleted question, it would have been in an answer. (See: Why can I not edit a self-deleted question?. This is also mentioned in the FAQ post: How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion?)
- The question has to be deleted too. (Otherwise your edits to the deleted answer would bump the question after each edit.)
- You should keep the link, otherwise it might be more difficult to find your draft later - especially if you're below 10k. (Users below 10k still can find a deleted post, if it was created not too long ago. More details can be found here: Is there any way to see my deleted questions or answers? Still, to be on the safe side, it might be better to keep a link somewhere.)
- If you edit the same post at least 10 times, then it is automatically flagged by the system for moderators attention. But I do not think that this would cause an actual problem. (There are certainly many posts which have 10 or more edits. So I am pretty sure that moderators are used to such flags and they only look into them if there is indeed something problematic.)
- As your question mentioned privacy, you should keep in mind that moderators and 10k+ users can still see your post, if they have a link. Of course, this can be sometimes considered an advantage - if you want some other 10k+ user to cooperate on the post.
- Although it wasn't specifically only about drafts, I have asked about somewhat similar usage before: Would using deleted (“hidden”) questions on math.SE for personal use be considered misuse of the site?
In any case, I can understand that some users might prefer have some other way to prepare a post than directly in the editor on the site. (And users who have been bitten by this in the past might be wary of relying on drafts.) Some users might use some other software instead on working directly on Stack Exchange. You can find such solutions discussed here: MathJax: better way to prepare a Math.StackExchange question?. (I have mentioned my own preferences on MathOverflow Meta: Is here something like blog service or just sand-box to store notes?) But some users might only have limited technical options or they might simply prefer the interface of the editor on Stack Exchange. You can see that there are users who use the sandbox quite often.
One other possible use of sandbox is if a user already posted a question or an answer and they want to do some extensive edits, which would lead to a lot of bumping of the same question. This is considered a problem, you can find these discussions on meta: How much (self) editing is too much? and Where is the fine line between using and misusing? You might notice that the sandbox was created around the same time as those discussions. I believe that the motivation to create the sandbox was (at least to some extent) exactly this issue. (Of course, the sandbox is still being bumped by those edits. However, bumping is limited to a single question on meta. Moreover, users can add sandbox to their ignored tags, if they wish to.)