Why low sensitivity speakers?

I found an article once, can't find it now. It said a high efficiency speaker CANNOT produce deep bass. Eg: Horns.

Karls, I learned a lot from your post. Could you explain something I have heard.

Listening to PSB Image 4T with plastic drivers, I was immediately disappointed to hear how much cleaner the sound was than B&W kevlar. But B&W's sales pitch is that Kevlar has benign breakup and plastic / metal etc. doesn't. That is, as the sound wave hits the edge of the driver and ripples back, the kevlar breaks it up while the plastic doesn't. The result is this reflected wave produces sound (which is not musical nor created by the input signal) and mucks up the true signal.

I can verify this as I have heard distortion on the PSB's which I think was due to breakup.

Is there any way to get the clarity without the nasty breakup? I asked B&W about this and they said using an aluminum driver, for example, the designer has to use a smaller driver to push the breakup mode higher and out of the range the driver is designed for. Even still, I have heard nasty ringing on small metal driver speakers.

I don't seem to hear this problem on Thiel speakers even though they have metal drivers and maybe this is because Jim Thiel is so obsessive about his crossover designs.

Would ribbon mid or tweeter drivers solve this problem?
Thanks, this question has bothered me for a while.

Thanks Karls, I will give this some thought. Zaikesman, the PSB were running on a Yamaha receiver/ Sony CDP. This was a store demo. Same music as the B&W.
I have the B&W in a different set-up and to the best I can say, the sound is not as clear as even the cheap PSB. Sound is much cleaner with low distortion, etc. but I don't think as clear.
It does not seem possible to get both sound qualities to their optimum potential at the same time and all the time. Take Revel for example. Some music they are great, other music they aren't. These are all my subjective opinions but B&W seems to be more consistent and livable across the board albeit sometimes sacrificing ultimate resolution.