Does the instantaneous frequency contradict the uncertainty principle?
The uncertainty principle works in the presence of (an uncertain amount of) noise or other signals (including possible harmonics), corrupting the exact phase, and thus the rate of change of phase of the signal of interest.  If the phase is corrupt, or mixed with the phase of other signals, then deriving an instantaneous frequency from the 1st derivative of that phase might produce nonsense.  Time-frequency analysis might be one way to (statistically?) separate information about the signal of interest out of these potentially existing "corrupting" influences.

Whereas the phase of a perfectly analytic signal including zero additive noise is better defined.