the length (time) does do a little something but it is still a static curve. Not exactly how a real cabinet would behave.
There's no measurement data that suggests this.
An IR isn't a curve in the colloquial sense of the term. It's a discrete-time signal, a sequence of amplitude samples at a fixed sample rate, typically stored in the same format as any audio waveform (typically a .wav file a few hundred milliseconds long at 44.1/48/96 kHz). It's the time-domain representation of the system's linear behavior, encoding every resonance, reflection, and decay with full phase information.
The IR, h(t), and the frequency response, H(f), are a Fourier transform pair. H(f) is complex-valued, containing both magnitude and phase at every frequency. Taking the inverse Fourier transform of H(f) gives you h(t); taking the forward transform of h(t) gives you H(f). They're two representations of the same information — one in the time domain, one in the frequency domain; neither is a static curve in the sense of a simplified magnitude plot.
A speaker/cab that plays an 80hz note from a stand still won't react or sound exactly the same as a speaker playing an 80hz note that just played a 90 hz note 20 ms prior.
That would require the speaker to be a system with memory or internal state that persists between notes. There's no measurement data supporting that. A guitar speaker is a transducer that responds to its current input voltage according to a fixed transfer function, it doesn't carry state forward from one note to the next.
The only mechanism that genuinely introduces time-variance is voice coil heating, and that operates on timescales orders of magnitude longer than 20 ms. There's no thermal effect in a speaker that acts on a millisecond scale.
The two scenarios aren't actually the same input situation. In one, the speaker is being driven by "80 Hz starting from silence." In the other, it's being driven by "90 Hz followed by 80 Hz," and the 90 Hz note's resonant tail may still be decaying when the 80 Hz note starts, summing with it at the microphone. That's not the speaker reacting differently — it's just two different inputs producing two different outputs. The speaker's response to the 80 Hz portion is identical in both cases. The IR describes that behavior exactly, which is why it reproduces both scenarios accurately.
There are going to be overtones and resonances in the cabinet and the cone.
The drivers themselves don't generate overtones in any meaningful sense at any normal playing level. A well-built cab shouldn't be adding harmonic content beyond what's already in the signal. If the cabinet is poorly made you might get buzzes, rattles, or panel resonances producing audible artifacts, but those are defects, not features of how a cab is supposed to work.
Resonances are a different matter; cone, cabinet resonances are linear phenomena; an impulse response captures them. An impulse response describes the cab's fingerprint including resonances, diffraction effects, etc as seen by the microphone at that position.
There is also the microphone interaction that takes part in capturing the sound.
Not sure what you mean by "interaction" here. If you mean the microphone's frequency response, its proximity effect, the comb filtering from the gap between the mic and the cone, and any reflections between the mic and the cab — all of that is part of what the IR captures. The IR is a measurement of exactly that chain: cab + mic + position + geometry, all baked into a single response. Whatever the mic "interacts" with during capture is already in the impulse response.
A guitar speaker cabinet behaves as a linear time-invariant system under any normal playing condition. This is measurable; you can verify it yourself.
Capture an impulse response using an exponential sine sweep (Farina method) with a clean driving chain with an amp and interface with minimal distortion of their own. After deconvolution, the harmonic distortion products separate out into their own discrete impulse responses in the pre-impulse region, cleanly isolated from the linear IR. You can window each harmonic order individually and measure exactly how much nonlinear contribution the cab is producing. In practice, for a guitar speaker driven at realistic levels, those harmonic IRs sit well below the linear IR in amplitude; the speaker is a linear device at the levels it actually operates at.
A guitar cabinet at realistic stage volume is being fed a small fraction of the amp wattage on average, nowhere near the thermal or excursion limits where nonlinear behavior becomes significant and awful sounding.
A common misattribution is treating the cab as the source of the nonlinear character in a cranked guitar rig. It isn't. The overwhelming majority of that nonlinearity comes from the amp. The preamp clipping, power tube saturation, output transformer nonlinearity, power supply sag. The cab is a mostly linear transducer reproducing whatever the amp sent it. An impulse response captures its contribution accurately.