Good speakers less efficient?

There are good speakers that are also efficient. While "good" is often quite subjective, some speakers that have been praised by some audiophiles that are also efficient include the Klipschorn, Avantgarde Duo, and Wilson Audio WATT/Puppy.

The low impedance characteristic is often the result of crossover design. The Thiel 3.6 is an example of a good speaker whose impedance dips below 3 ohms at certain frequencies due primarily to a design goal to preserve phase coherence.

Inefficiency can arise from crossover design also but is often due to driver and enclosure issues. The Acoustic Research 3a was a well-regarded speaker that employed an "acoustic suspension" design for its woofer. This sealed box design helped extract extended low frequency performance from a speaker of moderate size, something that was considered quite difficult to achieve at the time. The acoustic suspension design was inherently inefficient. (The AR 3a was also a 4 ohm speaker.)

I have not seen any statistical analysis of impedance and efficiency versus speaker quality. Would you share with us the basis for your cited "correlation"?

No stats, just observation. Nor did I say "all", but rather "many". Dali Helicon, Dyanaudio Contour, Harbeth, Totem Mani-2, some of the Tylers, et al.

Not looking for a fight, just information.

Not being a speaker designer, I have a fairly crude impression of how crossovers and drivers are used. My impression is that drivers function naturally over characteristic frequency bands, e.g., woofers only go up so far and start to drop off below a frequency inherent to their configuration and loading. Their performance over their bands is typically not flat. Designers use crossovers to boost and/or cut to smooth the speakers' frequency responses, as well as to extend performance beyond the speakers' natural bands, like coaxing a woofer to go lower. Beyond frequency response, designers also have goals for phase coherence (like Thiel), dynamic range, and low level performance, among others. This often results in unusual impedance loads and inefficient speakers. Nowadays, the availability of high powered solid state amplifiers allows the speaker designer generally to ignore such issues. The utilization of new speaker materials, like beryllium, diamond, or sandwich composites, allows the designer to achieve specific goals without as much complexity in the crossover and hopefully with less penalty in impedance and efficiency. I am hopeful other posters will have more specific responses to your question.