Anyone has a third option of saving a draft to their own files, for a text editor or word processor. I don't know of a third option within Stack Exchange.
But I don't understand exactly what's being suggested here and how this would help.
Who would be able to see a draft? Clearly the OP, but anybody else?
If there's a way of saving a draft that remains personal to the poster (and possibly a few key others, say moderators) until finally posted, then that seems a fair idea. Most of us are often in the position of the little girl who supposedly said "How do I know what I think until I see what I say?". It may take several revisions before we have expressed ourselves as clearly as we can. It's just a question of whether such a facility can be added (but I would guess wildly that something like that has already been considered and rejected).
However, a CV question is not like a research paper or report. If a question is long, my impression is that few people would read it. (In contrast, a long detailed answer is often especially interesting and useful.) I am tempted to say, contradicting myself, that if a CV question really requires multiple drafts, it's likely to be too complicated to have a good chance of a good answer. However, there are many complicating factors, such as people not writing in their own first language.
At present posting a question in effect should amount to a poster saying "I think I have here a fair question in good condition". Experienced users often disagree, as daily experience shows. A large fraction of questions are too general, too vague, too tied to specific data, too trivial, too badly presented, to attract much attention, let alone to be of much long-term use to anyone beyond the OP. So, what else is new? Helping the OP improve the question and deciding what is of value (including ignoring hopeless questions) is a large part of what the site is about.
But I wouldn't personally be tempted to spend much time on something labelled a draft. If the poster is saying "I know that this is in poor condition and needs to be improved", my attitude would be "Give us your best shot and then we will have a look". The tail of "I don't understand but the smart people on CV should be able to help" could be lengthened to include "I know this is not well written, but the smart people on CV should be able to rewrite it and then be able to help".