Right before they dive into that heavy math, they state that a capacitor driven by a sine-wave voltage source "behaves like a frequency-dependent resistance R = 1/ωC" – so I guess that's where I left it, conceptually.
Horowitz and Hill also state that:
Impedance is the "generalized resistance"... oversimplification of sorts.)
As you figured out, even from the best authors, simplification easily turns into over-simplification.
It is essential, at some time in your learning curve, that you fully grab the notion of current-phase vs. voltage.
But I would say that for understanding decoupling optimization, you don't need it. You just ned to know that capacitors are there to provide a low-impedance path for current variations. Typically, if a stage drives a 1kohm load, the capacitor's impedance must be an order of magnitude or two smaller than the load, AT THE LOWEST FREQUENCY OF INTEREST. That's basic math, and should not give you migraines
.
The difficult part is managing the path of the currents so they don't interfere with the clean path of signal - including the "ground"! (Don't forget the "ground" is the return path of signal. As such it is as important as what people commonly refer to the "signal path", i.e. the connection(s) from the output of a stage to the input of the subsequent.)
That means you have to see how current is sucked from the power supply pins, and how the capacitors will provide a preferred path to a common point, also see how the output current goes to the load(s) and returns back to ground.
Ideally this should be a real single-point of minimal resistance. It is generally easy to put the decoupling capacitors close to the opamp but it is much more difficult, and takes some experience, to make the return currents go back to the same place without interfering with surrounding circuitry.
Let's say you have stage that drives a fader and several aux send pots:
You must connect their bottom point back to the ground where the decoupling caps are, via track(s) that is(are) not used by any other circuitry.
PCB softwares ignore completely this constraint and will gladly connect the reference ("ground") point of an EQ to the same ground than the fader send. That's why a good AUDIO designer will route the "grounds" manually according to the PCB topology, and run the autorouter subsequently.
The copper pour (ground plane), done without caution, may well ruin that plan; again, it takes some experience to create the necessary channels and islands in the copper pour that will make sure there's no undue short-circuit between "grounds".