helmet fire is right. There are some aerodynamic causes limiting the airspeed and the performance. Greater airspeeds with removed doors could go up to problems controlling the bank of the a/c. Due to the greater drag and the influence of the changed airstreams to the main AND tailrotor, the performance isn't as good as with doors closed.
Cat A with opened / removed doors is also not certified on BK 117 and EC 135.
Integrity and chrashworthiness of the cabin is is abolutely given also with opened/removed doors. There is a carbon frame on EC 135/145 giving the structural integrity. The doors doesn't have structural influence.