"What role does impedance have, if any, alongside other factors in the calculation of how much power should be used to drive a speaker comfortably?"
Zero, because in my experience, the math is not complete. We don’t get damping factor for the amp, most of the time, and it too, is frequency dependent. In addition, my experience says that amps are more sensitive to impedance dips than the math would lead us to believe if we did know this.
The way to approach this is, for a given speaker, note where the impedance is worse, then listen to amps with music in that range and see if you hear or feel the deficiency in amplifier output.
One speaker I feel is notorious like this is Focal. They often have these narrow dips around 100 Hz and anything but the most robust amp will noticeably sag.
One decent indicator of an amp’s current drive (ability drive low impedance speakers) is how well it doubles power as impedance drops in half.
8 Ohms -> 100 W
4 Ohms -> 200 W
2 Ohms -> 400 W
But again, I feel noting the impedance dips and listening is a better indicator than this.
Best,
E