Speaker sensitivity vs. sound quality vs. size

All these discussions about Tekton speakers and their sound quality intrigued me to ask the question if there's any correlation between speaker efficiency and sound quality. I'm also throwing the speaker size in the mix because the specific Double Impact model is quite big and heavy but still has an incredibly high sensitivity and apparently sounds real good. Are there any benefits in building a speaker that is very inefficient, like many high end Italian manufactures do. In other words, why wouldn't all designers follow the general Tekton recipe. For the sake of this discussion, let's leave out planar models since they are intrinsically inefficient by design. Sorry if this question has already been asked.

generally speakers in the early days of audio had very high efficiency because the amps of the day were low powered also the speakers were quite large. To get more bass out of smaller speakers the efficiency dropped as well. its easier to make high efficient larger speakers then smaller ones but most people don't live in theaters so speaker designers designed speakers that were smaller and took advantage of the new (70's) SS amps that had more power. But as Tube's have made a big come back and lower powered ones seem to be also coming back full force, speakers makers are once again designing higher efficiency speakers and they tend to be larger ( if you want full'ish range) but that's not always the case.
Inefficient speakers hide the noise in the system.  :)