While leaving comments are helpful, I don't believe it's critical that the same person who voted to close also be the same person who leaves a comment.
On a site where all of the users are volunteers, distributing this workload among everyone can help lighten the load and create a more sustainable process where more people are involved.
As I mentioned in the other thread, we can comment on posts we didn't vote to close and leave suggestions for improvement, even if we believe the question should not have been closed.
The other concern is that not everyone is a good commenter. There are certain people whose skills may not lie in coaching others. Some people aren't good at disarming conflict that may arise from comments that were taken the wrong way or misinterpreted as "hostile".
In short, I'd never wish to see comments be required -- which of course isn't what you're proposing -- and as long as it's clear that comments aren't required, it may be helpful to display a popup encouraging that a close voter leave a comment suggesting ways to improve the post. If that person can articulate a helpful suggestion, then he or she should by all means post a comment, if he or she has time. :)