I would say, that yes, it is good to have "faith" unsupported by reason. To me, again, only for me, faith is not a thing of reason or logic. In fact it is quite the opposite. However faith should not be a foolish thing, going back to the tree, if I stand under it as it falls expecting God to stop IT or move ME, that is not faith, that is suicide in denial. I do however believe that after the tree squishes me like a bug that the God of my understanding would collect my immortal remains and deal with me accordingly, probably starting with a speech about dumping funeral expenses on my unsuspecting family.
I dont mean to imply that I know anything no-one else knows, faith in anything is a constant struggle for me, I am not a great thinker, I hold no degrees or letters of merit, I didnt even graduate high school. I am just one man on a personal journey. I dont think I would want any kind of "faith" that would stand up to logic or reason. That would make it just another Google search result.