This is the exact opposite of reality.
High output impedance means as the speaker impedance varies through the frequency range, so the output of the amplifier will vary as the output voltage is divided between the output impedance, and speaker impedance.
High output impedance will create a very non flat FR at the output of the amp.
Agreed.
However, its not the voltage but current that drives the speaker. So its worth taking a look at the power response instead of FR (frequency response).
In the attachment, in table 1, the output voltage of the amplifier is the voltage appearing across the speaker. Power delivered into the speaker is calculated as speaker impedance varies from, say, 5ohms to 12ohms which is not uncommon for an 8ohm speaker. It is seen that power decreases as speaker impedance increases. The variation in output power is from 0.2W (@5ohms) to 0.083W (@12ohms)
Now consider, say, a 1ohm resistor in series with the loudspeaker. This arrangement will create variable voltage across the speaker as the speaker impedance varies, just like what you said in your post above.
Attached table 2 calculates power delivered into the loudspeaker with this new arrangement for the same speaker impedance variation from 5ohms to 12ohms. The variation in output power is from 0.1388W (@5ohms) to 0.071W (@12ohms)
To make interpreting the results easy, allow me to increase the volume (and hence the amplifier output voltage from 1V to 1.2V) to compensate for the loss in the series resistor . This is shown in table 3. The variation in output power is from 0.2W (@5ohms) to 0.102W (@12ohms)
Variation in power delivered into the loudspeaker has reduced as compared to a pure voltage amplifier with zero output impedance. This is the point I was driving: To make power delivered into the speaker depend on input signal and input signal only and not on loudspeaker impedance variation. This should be the goal and this does not happen in reality.