Atmasphere, In that most (all?) speakers draw power with varying impedances and those impedance changes will correspond with sensitivity changes (again we're talking about typical speakers here) unless the amp(s) can change power output appropriately there will be deviations from linear frequency response.
Yes- and enough global negative feedback will allow nearly any amplifier to do that. Its not about being able to double power, its about the amp being able to act as a voltage source. Plenty of tube amps can do that. If we add about 20 db of feedback to our amps they will act like a voltage source too.
Again, the amp does not have to double power as impedance is halved. What it does have to be able to do is cut power in half when impedance is doubled in order to behave as a voltage source.