Ok, I have never flown a helicopter but have time in General Aviation aircraft and can tell you this;
If I tried to fly a plane using the keyboard I would inevitably crash (considering all forces acting as they should and even atmospheric variables but i'll leave the atmospherics out for now).
Yaw is going to be there from the start as it is caused by;
Torque reaction from engine
Spiraling slip stream
Gyroscopic action from the propeller, and;
Asymmetric loading
Assuming JSBSim modelling is accurate then by default you will need a variable rudder input which is a constant requirement in any aircraft in many situations. Simple controls would need to be set to disregard the yaw effect which is most likely the effect you are experiencing with the chopper. Yaw can also lead to a wing drop (among other factors) but can cause all sorts of problems to maintain straight and level flight at the bare minimum.
Perhaps even an auto-trim for those who don't wish to bother flying as per real world. Otherwise, the appropriate hardware is required, nothing less, if you wish to experience most/all the forces acting on the aircraft.
I can tell you it is much more challenging to experience these but acknowledge more frustrating for those who either don't understand the aerodynamic concepts or are more concerned with the scenery out the window rather than constant handling of the aircraft.
I can say that very little time is spent out the window when flying IRL as there is much to do and focus on to maintain proper handling of the aircraft. In a simulated environment there may be less interest in these areas but I personally enjoy the accuracy of flight dynamics over ease of use.
A setting just may strike a balance between those who just want to fly the aircraft and those who want to tackle the challenge of true flight.
Cheers,
K.