Exactly. I wrote this explanation, but you beat me to it, so I'll just post it here:
The real reason we use I/Q sampling is because we want to frequency-shift a signal.
Why do we want to frequency-shift a signal? In radio frequency applications the signal of interest almost always has a much lower bandwidth than its highest frequency. In other words, the signal has a small bandwidth (say 40 MHz) centered around a high center-frequency (say 2.4 GHz). If we want to digitize the signal, then one way would be to use a very high sample-rate ADC (e.g. a 2.4 GHz ADC). But these are very expensive, and a much better way of digitizing the signal is to use a mixer (a frequency shifter) to shift the signal to be centered around 0 Hz and then use a relatively low sample-rate ADC (e.g. a 40 MHz ADC).
The way frequency shifting is done is by multipling the signal by a sine signal, which can be done in hardware. But this introduces a distortion to the signal because multiplying by a sine is not actually a frequency shift. It just so happens that this distortion is cancelled out by adding another copy of the signal multiplied with another sine delayed by 90°. But this addition needs to be complex (due to the relationship between sine functions and true frequency shifts), so what we do is sample the two distorted signals and do this complex addition with the digitial signals.
So the reason we have complex samples is because that's the best way we've found to do frequency shifting using real-only sine waves (this explains why we don't use complex numbers in audio signal processing; there's no need to do frequency shifting!). This tutorial goes into the details and is the best explanation I've seen on quadrature sampling (another term for I/Q sampling): https://www.dsprelated.com/showarticle/192.php
I think engineers (myself included) tend to get confused because using complex numbers makes the math simpler, and so they think that's the real reason we use them. All the talk about ambiguous frequencies or negative frequencies or needing to know the phase of a sample is true, but all of those problems could be solved without complex numbers simply by sampling twice as fast and then doing some math (again, audio DSP does just fine without quadrature sampling), so it's not a "real" reason to do this strange kind of sampling.