At the same EAS at 35,000' or at SL, the control effectiveness should be the same. But apparently it's not due to the density of the air...?
There's not much difference in control efficiency itself at same EAS, until some serious aeroelasticity and Mach effects take place. We'll disregard them. Problem is not controllability but stability, namely natural damping coming from vertical stabilizer decreasing with altitude due to sideways angular displacement of stabilizer (a.k.a. yaw) remaining constant while TAS increases. Even with constant EAS, vertical stabilizer AoA is lower at higher TAS, therefore decreasing the force on the stabilizer and with it moment that opposes the yaw. That's where yaw damper comes in - it has to work harder at higher altitudes.
Handling the big jets, pages 162 to 164 explains it nicely. Principle is applicable to any aeroplane requiring yaw damper, it's just more critical on big jets due to their higher speed.
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