ehsjr wrote:

The discussion has nothing to do with ideal components.

Actually, in the end, Laplace-transform (impedance methods) circuit
analysis is calculated based on ideal components, the only ones whose
behaviour follows practically simple mathematical rules. The question
is simply how much effort we need to make to represent any real
components we are using by sufficiently detailed, situation-adjusted
models made up of varied ideal components.

How do you calculate the impedance of an inductor that can saturate in
a way that reflects this? The answer is that you can't, you can only
calculate an effective impedance under known saturation conditions -
which is to say that your junk box inductor is represented by an ideal
inductor of a value which depends on the degree of saturation (and
other ideal components if we need to model series resistance,
distributed capacitance between turns, etc)

The magic words in circuit analysis are "linear time invarient". If
you have something that isn't, you either do a lot of messy
calculations (probably only practical numerically), or you figure out
the steady state conditions of its operation and devise a small signal
linear time invarient model reasonably accurate in that regime.