Speaker impedance and sensitivity

This is an old topic but I'm curious about the notion of "easy to drive" speakers that are labeled so due to their benign impedance curves. I understand that such speakers will draw relatively less current from the hypothetical amplifier. Does this mean that regardless of sensitivity the speaker will play to its full potential up to a certain point?

Good examples are British monitors that generally have high nominal impedance but often brutal sensitivity ratings. These speakers should be "driven" well at moderate volumes but simply won't play loud unless paired with a really powerful amplifier. Am I thinking about this right? If I am, then audio enthusiasts should consider how loud they listen when choosing an amp and open up a wider range to choose from. Comments please. Thanks.