When the original author of the question tries to close it, does it still require 4 more votes? It would make sense just to close the question if the request came from the original author.
Check out this CW on SO
Specially this quote (by Euro Micelli)
I agree. I've wanted to move a few of my questions here to Meta, but I need at least 4 other people to help (or a mod).
However, there are a few issues that would need to be worked out should that user decide to open the question back up. If the owner closes their own question by themselves, should they have the power to open by themselves? If so, what if there are already close votes - closing and reopening would effectively zero out the votes. Maybe if a question is closed by X people (say 2 people + owner) then it would have to be opened up by X people?
In any case, there are tricky edge conditions to be aware of, but I think that if you can delete (and undelete) your own content, then you should be able to close and open it as well.