I agree in essence with the premise: that often new users are down-voted into oblivion without any constructive feedback that they can use to reverse that trend. This is in part because the right to down-vote comes long before the right to VtC, but also partially due to other reasons, such as (a) the effort it takes to decide why they VtC, especially with the new close reasons; (b) not caring at all; (c) not wanting their name to show up on the "closed by..." banner; etc...
However the exact implementation you suggest is problematic just due to the complexity of changing all of those pieces (never mind how it flies in the face of the status quo).
While I do agree that some people might down-vote a question that they feel should remain open, I tend to do the opposite: I vote to close before I down-vote. This automatically gives them the feedback they need to improve the question (if possible) without punishing them for it (at least in terms of reputation). If I remember to revisit the question and it's still open but still in terrible shape, I will probably down-vote more for the lack of effort than anything else. So in some cases my down-vote might be completely disassociated with the close reason. And I'd want to maintain my ability to keep those separate. Especially here on meta.
Unless you're the 5th or binding vote, voting to close doesn't actually close the question, it just gives the user a warning. On SO there isn't much difference since dog-piling usually leads to a very quick progression from 1st to 5th close vote, but on other sites there is usually enough time that the user can do something about it - if they want to and know how.
And if you want other ways to make people explain why they down-voted, you can probably forget it:
Encouraging people to explain downvotes