Should our students be Writing their own Tests

Could our students be using tests as learning tools as well as assessments?  For years schools have given tests to students to assess what has been taught.  Students study, take the test and forget it. The information regurgatated for the test was useful to that student only for a short time.  They get good grades, but are they learning anything.  I'll use my loving wife for an example.  She was always a good student. Honor roll, top of the her class.  I on the other hand never made the honor roll, I don't even know where I was in the standings at graduation. And didn't really care.  But, most of  what I learned, I can still remember today.  She on the other hand can not. 
Some of our students are very good at What and When questions.  But the Why somehow eludes them.  Others, can explain why something happens, they can see the relationships among the facts and understand how the facts had become facts.
Most tests our students are given are what and when tests.  They don't give the "why" student the chance to shine.
Maybe we should start having our students write the tests.  They would reflect what the students learned and could be a cooperative experience for the students.  Grouped students would write questions that would reflect their learning style. Everyone would be able to show what they learned.  They could act as learning tools as well as ways to give grades.