Well stated and quite the case in my opinion also. It is the reason I have had up to 40 headphone amps at one time (not counting the ones I have for my electrostatics).Hmmm... any device can "drive" any headphone. Your cellphone can "drive" a 600 Ohm T1.
But depending on how you define "drive" a headphone it is not an either or... some amps sound best with 600 Ohm impedance, while they do not sound great with 32 Ohm Grados, some amps pair better with low impedance. To me the pairing and synergy is the real matter of the case more than price and power specs of the amplifier.
I used to say to my buddies it was like having the right seasoning. The only reason cost was a factor was the condition of my wallet at the time. Some of my best matches were far from my most expensive pieces.
The Quest continues as it does for many of us.
Have fun.