What's the problem with being lazy? If you are even lazier, just don't answer. If it's a duplicate, just link it to the delicate question. Having useless questions shouldn't be a problem while searching for answers.
The problem is that just looking through the queue of unanswered questions takes effort.
If I have a list of good, honestly-asked questions, I'm willing to look for a few that I know how to answer and answer them. If I have a vast pile of "plz do this homework for me [transcribed question with errors or link to a private PDF]" then I just won't use Stack Overflow.
All SO tags I've ever followed the number of people answering is greater than the people asking, so that's not really an issue, I think. Although, maybe, it felt that way due to down voting.
The case you described is easy to identify and you can just leave a comment, which will be useful to both: other people answering questions and the person asking. Different from the down vote.
Roughly, it seems downvotes are used by people to indicate not enough effort has gone into the question (easily researched, duplicate question, confusing/poor english, etc).
So either all unflagged questions is valid and should be nurtured into clear, well-written queries or pointed to existing questions, or questions are to be judged* "good-faith" or "lazy" by users and the latter receive downvotes.
*This judgement is fixed in time; the question is not necessarily re-judged if improvements are made.