Mr.T wrote:
Thinking about speakers ..... say connected to an 8ohm
rated amp. If they were 32 ohms, then the amp's possible
power would be was less (than if the speakers were 8 ohm)....
25% of the power, to be exact.
Only if you ignore Current limitations.

Say you had yourself an amplifier that was rated at 100 watts
into 8 ohms. That means that it could swing 28.3 volts RMS
into that load. Let's say 30 volts to make life easy.

At 100 watts, it would be putting about 3.5 amps into that 8 ohm
load.

Now, let's say said amplifer has an ultimate current capability of,
20 amps continuous. That would mean that it could easily do
7 amps into 4 ohms, which could be 200 watts, and it could do
14 amps into 2 ohms, corresponding to 400 watts.

Let's go in the other direction: how much current could said
amplifier put into, say, 32 ohms (just to pick a random number)?

Given that its output voltage is limited to 30 volts, the ABSOLUTE
MAXIMUM it could put out is 1 amp. 1 measely ampere. That's it.
Doesn't make any difference what it OCULD put out, 32 ohms
ain't gonna let it put out any more. None. Zip. Nadda.

But, what if you REALLY wanted the full 20 amps into 32 ohms?
Herr Ohm tells us how:

E = I * R

E = 20 amps * 32 Ohms

E = 640 volts.

Do you know any amplifiers that can swing 640 volts RMS?

What about current limitations?

The voltage limit imposes the current limitations at high impedances.

So why is it so?

Ohms law. Any amplifier is limited in the amount of
voltage it can put out.

What amplifier has infinite current capability? Any amplifier has both
voltage *AND* current limits.

Yup.

At high impedance, your voltage limit dominates. At low
impedance, you current limit dominates.

The higher the impedance of the
load (speaker, headphones, incandescent lamp, etc.,)
the less power the amplifier can source into the load.

Not necessarily. Many amplifiers will provide higher power
into a four ohm load than a two ohm load for example.
Some even provide higher power into 8 ohms than four,
due to low current capability.

Are we having fun?

(Of course their aren't too many 4 ohm headphones, but your comment
specifically mentions "speakers, incandecent lamps etc.")

Nor is there anyone on this planet that would want to dump the entire
power of their amplifier , whether it's at current limiting or voltage
limiting, into their headphones. Our hypothetical 100 watt amplifier,
which we know can produce 30 volts across 32 ohms, would generate
a nice sound pressure level of well over 140 dB SPL into your typical
headphone.

Given the context of the discussion, which I agree is only weakly
hinted at by the word "headphone" in the subject line, does your
particular thesis make a lot of sense?