I imagine that they have something to tell, time to time, about the reasons why they did what they did and comment on the state of the society. And I don't believe that we gather the findings and then communicate them back to the policy makers so that we are actually able to heal the society.
I mean, there is an argument to be made there. If people are lashing out violently, they've probably run out of non-violent options and that's something that should be addressed. But I think it sets a horrible precedent to allow violence to shape political discussion.
Understanding what drives a terrorist does not necessarily negate any punishment for the act of terror. It does give you the opportunity to decide whether the grievance that led them to act is one that you agree is legitimate, or if not, perhaps it is one that you want to address anyway in the interest of lowering the risk of other terrorist acts. All of this can be done without excusing in any way the act itself.
Second, I find it odd that you think putting killers in jail is "a waste". Should we just let them go and have another try?
Last, you assume that these individuals murder innocent people because they have some valid point about society, which policy-makers need to learn and act upon. What point would that be?