Engine failure is not an issue for climb rate, as all these helos are twins, and do not have to suffer simultaneous dual engine failure.
The climb rate restrictions are almost always handling qualities, longitudinal static stability. In high climb rates, there are weird little areas where the tail falls under the main toror downwash, and the nose attitude actually trims up as speed is increased. This is no problem for pilots, but boggles the requirements for "stick stability".
Also, the airspeed system has to meet some accuracy requirements, and at high climb rates, it can fall under the main downwash, and make unacceptable shifts in its calibration, or get really jumpy.