Some examples would be useful, but I must say I don't really share your concern on this. I don't see many off-topic questions answered here.
At the same time, I do see quite some questions marked off-topic incorrectly. There seems to be a tendency to close-vote on trigger words like bug or the current +1 release, while the issue in the question has nothing to do with version-specific issues or -bugs for example.
Furthermore, I consider an unjust close vote a bigger sin than incidentally answering a question that could be marked as off-topic. In the first case, you send someone away who could (and should) get an answer here, in the latter case, the worst thing that can happen is that a good answer is given at the wrong place.
I don't see your issue that it invites people to post the wrong type of questions here at all. When people post questions that really don't belong here, it is because they are not familiar with the SE sites, not because they looked through this site's variety of questions.
On the contrary I would say, in general these people are not familiar with the site at all.