Does the instantaneous frequency contradict the uncertainty principle? The uncertainty principle states that there is a trade off between time and frequency. So, finding frequency components at specific time is impossible. However, the instantaneous frequency measure the frequency as a function of time. Which means using the instantaneous frequency, the frequency components could be found for a signal at a specific time. How can you interpret this? Why don't we use the instantaneous frequency for time-frequency analysis?
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.