The model you are proposing relies on propagation time being mutable, which it certainly is not.
Atmasphere, forgive me if I'm being a snot . . . but I think you need to brush up on some basic electrical theory. Pole/zero networks do indeed have different delays based on frequency. If you don't believe me, try constructing a simple R-C lowpass network with, say, a .47uF capacitor and a 750 ohm resistor. Compare the "Propegation Delay" between input to output, using SINEWAVES, at 10KHz and 20KHz. For the former, you will find it to be about 24uS, for the latter about 12uS. For both, the phase shift is about 90 degrees. Or you can do it in SPICE in just a few minutes.
Again, some basics here. A real-world amplifier circuit contains mechanisms that produce both frequency-dependent and frequency-independent delays. In a typical well-designed Miller-compensated amplifier, the goal is to choose the compensation capacitor so that the frequency-independent delay is completely swamped by the frequency-dependent delay of a first-order slope, yielding a phase margin of 90 degrees at all frequencies above unity gain.
Here's the conceptual error with your square-wave timing test. If we assume that it's indeed a perfect square-wave on input, and the circuit in question doesn't have infinate bandwidth . . . then the output square-wave will have a longer rise time and more rounded leading edge than the input. So we set up our scope, and use the markers to decide where to measure on the x-axis. For the input side, it's easy to locate the marker because the rise-time is infinately short. But on the output, it's comparatively slopey and rounded . . . so when you look at the output and place the marker, the exact placement across the slope determines for which frequency you're measuring the delay. If you just place the marker where it "looks about right", then you're simply meauring the delay of "kinda one of those frequencies" . . . one of an infinate number contained in the perfect squarewave on the input.
But really the time-honored method is to use X/Y mode on your scope to compare the phase as you vary the frequency of a sinewave. You can then CALCULATE the precise delay for any frequency, based on phase. And no, there won't be just one number.