I think any means to make users use the search option reduces the number of duplicate questions. Therefore, I propose to encourage its use.
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Although this is an interesting idea, I would suggest to not make the change for the following reasons:
Users who don't know that they should search before asking won't know that there are badges either.
Searching before asking is a common etiquette of all online communities and is better known to general public (i.e. new users) than badges.
Besides, I thought that badges were to be awarded for promoting good behavior. This would be promoting the absence of bad behavior.
It's like giving someone award for not robbing a store. It is expected behavior, not exemplary good.