I agree with Mika. How do you feel when someone tells you that your application is bad, sucks, doesn't work etc. and offers no specifics? A demote without a comment has negative value. It's all noise, no signal. A value with specific comments has positive value, more value than any single promote.
@5 - Exactly, constructive criticism is the best a developer can get. He assumes his product is working fine, so positive comments are nice to hear, but they don't make the product better in any way.
The problem is, you can't enforce constructive criticism. Put in a requirement to comment when voting "No", and you'll see more "I disagree" comments. We need to trust people, and enforcing a comment on negative votes just gives the message that no justification is needed for voting for ideas, while justification is needed for voting against them. The cost of voting "No" is therefor slightly higher, which actually reduces the value of the results. Imagine if everybody just voted "Yes" on each idea. The site would fade away very quickly. A requirement to comment on negative votes would not kill the site, but it would encourage the idea of no cost for voting "Yes". If anything, I'd prefer a limited number of "Yes" votes to match the realities that we have to make choices about how time is expended, not fall into the trap of thinking that all changes are cost-free.
I don't believe that requiring a reason for the "No" is too costly, especially since there is a "No Opinion" option. As I've gone through some ideas, there have been relatively few that I felt were a real "No" (and, I believe I explained my choice in those cases.) If I didn't have a strong "Yes" or "No" feeling, I would pick "No Opinion."
I agree, however, that the required comment could just be gibberish, unhelpful, or even abusive.
I agree with @8, we've chatted about this issue before and came to the opinion that forcing people to leave a comment will not actually add any benefit. In the end I think demotes with an opinion will probably carry more weight with the idea proposer and the rest of the community.