Please just acknowledge that an x-over doesn't pose a problem in time domain, and that single wide-band drivers exhibit at least as much phase alterations to the original signals as non-pathological multy-way speakers do. In case you don't it is your turn to deduce a fully connected chain of arguments for your claim, as my stance is supported by all the literature.
I'd like to address this in two parts.
First part:
If a single wide-band driver and a multi-way both have the 'same frequency magnitude response', their phase alterations will be the same at the ends of the spectrum.
The same 'frequency magnitude response' means both speakers have the same low-end and high-end frequency response roll-offs.
But those system roll-off regions, are the only frequencies where phase alterations will be the same.
In between, through the main spectrum, their phase alterations will not be the same. (other than special cases where the multi-way uses only first-order IIR or linear phase xovers.
The single wide-band driver will have flat phase, due to not having any xovers.
The multi-way will have phase rotations depending on number of ways/xovers, and crossover orders.
Second:
I agree that a xover doesn't pose a problem in the time domain.
Because my definition of 'time domain' is just that...
time. As in seconds, milliseconds, microseconds.
An impulse response shows signal amplitude vs time. Doesn't show either frequency magnitude response or phase.
FFT math derives frequency response from the impulse response...and freq response is defined as complex freq response which includes freq magnitude and freq phase.
My intended point here is that
phase is a component of the frequency domain...and not of the time domain.
Time is a constant. Phase is a rotation of frequency's relative cyclical alignments.
They are simply not substitutes ime, one for the other.
The idea that phase can be equated into a unit of time for a given frequency, and then used as a substitute for time alignment....
.....is a very suboptimal but appears oh so commonly used in IIR xover design.
Ok, off soap box and back to topic...
I say xovers pose no time domain problem. They cause a phase rotation problem. (other than first-order IIR or lin phase)