Here we have an explanation:
"Weidemann's explanation for why battery-powered devices perform best with low-impedance headphones is based on this: Most portable players use from 3-volt to a maximum of 5-volt batteries, that means the signal voltage at the output is low, but they can still deliver high current with low-impedance headphones, and the sound will be fine. However, if you plug in a high-impedance headphone to a portable device the voltage and current will be low, so the headphone won't play loudly at all, and dynamics will be reduced."
https://www.cnet.com/news/headphone...d-to-know-about-low-vs-high-impedance-models/
Additional info:
"It's not an opposite logic, it's rather that speaker range between 4-8 ohms while headphone are more like 30-300. With speakers you'll get amperage problems while headphone will ask more voltage. "
and
"Both are extremes - Speakers have very low impendance to begin with. 8 ohms being fairly standard and can drop to even 1 ohm. Headphones have very high impedance 30 - 600 ohms. So at the extremes 4 ohms or less and above 300 ohms, you are asking a lot more from your amp (for different reasons).
I know with headphones the challenge with high impedance is getting sufficient volume out of the headphones. Since the higher the impedance, the less power (wattage) the amp produces. So if you want to use your headphones with your phone/portable device you want to be closer to 30 ohms. If you plan to use them with a dedicated headphone amp, then 600 ohms is your best bet. "
This speaks to me a little more - in addition to the obvious important sensitivity/efficiency spec you mentioned, for determining drivability.