If a toy gyro isn't rotating at high speed it falls over so it does matter.
OK, and it matters how exactly? The gyro forces at low decreasing RPM get weaker and weaker in comparison to the constant toppling force, until at some point the latter dominates the former and it falls. How does this slot into the arguments that I or you have been making?
Of course you can but that is just applying additional torques and muddying the waters of what is discussed here
Yes exactly, "applying additional torques" is the reason a toy gyro in my hand moves at angles different from the ideal 90 degrees. Here, it's easy for you to disregard the additional torques, and consider the base mechanic by itself. To avoid muddying the waters, you carefully examine the separate elements and their relative contributions to the total behavior. Though the base 90 deg. interaction is modified by the additional torques, you see beyond them to the base mechanic itself, which is gyro precession by definition.
So when a rotor, due to "additional torques," is also modified from the ideal 90 degree behavior, why can't you disregard the additional torques and see the base behavior as readily as you do for the toy gyro?
Why is the toy gyro in that case still a gyro, while the rotor is not?
Actually I see two different possibilities for our disagreement here. Maybe you can tell me which it is, or some third one I didn't think of.
1. You do see the base behavior the same as that of a toy gyro, but just don't want to apply the word due to the presence of the additional torques and modified behavior. So we recognize the same mechanics, and it's a disagreement only over the label.
2. You do not think the base behavior of a gyro is there at all (or is there, but in some hugely diminished proportion to the additional torques), so the disagreement is not merely over the label, but over the physics itself.
On a rotor, the mechanical input is the start of the process, the next stage is the aerodynamic forces [normal force] that are a result of the mechanical change in pitch to the blades - these accelerate the blades [beginning at the point where the normal force was applied], assisted by the mechanical input and governed by the laws of aerodynamics - the movement eventually cancels itself out when the lift produced is negated by the braking/damping effect of the air [other normal force is applied later] and the reducing mechanical input.
I'm not sure where you were going with this, but I just added little annotations here to get us on the same mental track in talking about the same thing, if you care to expand or show an inference.