Yes. Don’t confuse phase shift with time delay. Not so easy if the crossover filter is IIR Biquad and phase of each driver not known precisely. With FIR filters, one can completely compensate the phase first to be flat and the same for each driver - assuming you that extract the minimum phase of the driver correctly first. Then setting the delay so that the signal from each driver reaches the microphone at the same time is straight-forward. But in this process ^ you have to do the phase compensation before time alignment first.
Yes indeed
Time delays and phase are simply not substitutes for each other.
And as you say, for aligning drivers, get the phase of each correct first, then time align..
Hopefully this example of that finds some interest.......here's the acoustic measurements acoustic of a 5-way's passbands.
Each passband was first individually tuned as a linear-phase passband. So each has flat phase at zero, throughout its passband and summations.
First without time alignment.
With linear-phase passbands, time alignment requires impulse peaks align. The physical design of the speaker happended such that the blue low driver and green mid driver need very little delay between them, as their impulse peaks are close together. The purple sub needs the most delay added. Orange and yellow HF and VHF need less, but it's clear they need slightly different amounts of delay due to small null at xover.
The solid black line is the summed acoustic response. The black dots are what summation could be with proper time alignment....which follows blows.
Proper time alignment of 5-sections. All impulse peaks aligned.
Note passbands' responses don't change, just the summations change.
Hope twas of interest...