There are actually a few things going on here again, so let’s see if I can explain in a few sentences what it took me an entire 4 credit college course to understand, because there are different vectors involved here. I'm thinking that maybe the better way to illustrate this is by looking at the system in full rotation, then trying to change the direction, instead of trying to illustrate the relationship of forces going into creating the rotating system.
The reason why it is so easy to balance on a bicycle when the wheels are rotating as opposed to trying to balance on it while sitting still, is a result of a few of these rotational vectors and inertia. This is similar to why a gyro on a satellite keeps it from wobbling, but it also has to do with the fact that trying to make a rotating object move in a completely different direction from how it is initially rotating, takes force. So once the wheels are spinning at a high velocity, changing the rotational direction or angle means you must add more energy to the system. So once the Funny Car wheels are turning and facing in one direction, they will tend to stay in that direction. The same reason is why you lean on a motorcycle to turn, instead of steering with the handlebars -- which would change the direction of one of the spinning wheels which is something the wheel will resist. But according to Delta L above (change in angular momentum) a monocycle (one wheel only) will try to precess around the seat in accordance with the right hand rule – where you wrap your fingers of your right hand around the shaft in the direction of rotation and your thumb points in the direction of Angular Momentum L. The difference between the direction and force of angular momentum and the direction and force of the torque vector is the force that precesses the shaft to the left.
In an airplane, the angular momentum and torque are acting together to create a resulting force vector. If you try to turn the plane in any direction, the prop still wants to maintain the same rotation and attitude. So in a KE spin, where you are forcing the plane to rotate in a way that is counter to inertia and the forces being applied by torque and angular momentum, you are forcing the prop and motor shaft to go in a direction it does not want to, and it will resist. Forcing the prop and shaft to change directional attitude in an electrical motor setup can cause magnets to collide without support and bearings that can handle the input force, etc.
Some planes can only KE spin under full throttle because of the force needed to do this. Some effort also is needed to do rolling harriers in different directions because the force is different in one direction than in another.