Speakers The single most critical component

Certainly one thing I could learn from you is how not to communicate. I also could learn how not to present a discovery if I wanted it to be taken seriously. Far too many definitive statements, far too many generalizations and a grand oversimplification of something which is very complex. I dont disagree with your basic premise, just much of what  you puked after the title of the OP. I think some basic advice on presentation is very constructive. I mean it really wasnt a discussion just you monologuing. 

Mozart fan
I think reducing an evaluation down to one aspect - efficiency- of the many issues to consider is not the idea. Its like saying you'll only consider a car that gets over X miles per gallon as a proper car.  What if you want a sports car?  Or if you want a truck to haul things?  Different motors, different efficiencies.  Efficiency is NOT the only thing that matters in engines or drivers. 

From product management experience at JBL and with ATC, a driver can be optimized for bandwidth OR efficiency.  If you want more low end from a driver, it WILL be less efficient.   IF you are willing to forgo some low end, you can go for efficiency.

I know for example ATC SCM19/20 systems average 87dB SPL 1w/1m.    In its sealed box, that 7 inch SL driver has response down to 30-40 hz.  Why give up this low end for a higher efficiency when amp power is so affordable these days?  Its not like the old horn days, where a 70W amp was about as large as they get (at least in tube power amps).  

Brad        

box, that 7 inch SL driver has response down to 30-40 hz. Why give up this low end for a higher efficiency when amp power is so affordable these days?
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Well some of what i said above has tp be qualified, re-hashed in view of further considerations.

Agree if you can find woofers, especially in the 7-8 inch range which deliver solid bass with clear low mids, (crossing say no  higher thahn say 2k), here db level is not so important, My seas W19E001's with new Mundorf Supreme Silver caps,  have increased the performance of the woofer. Seas has  the W18E001 rated 87db. With the old Hovland caps, the bass was not as punchy.
Not sure how to explain what the Mundorf caps a 10uf+ 2.2 uf have added to the W18's performance, but its superior bass vs the old cheapo Hovland 8.2 cap. 
Its really in the midrange and even more in the say,,,,12k+ fq's where sens really beccomes a  critical issue. 
So far my testing of some cheap chinese *FR* drivers has given me some insight how the sensitivity rating becomes so important.
Also the use of a  Magnovox tweeter horn, guessing 96db sens, also has proven to be a  superior speaker vs a  say 90db/under dome tweeter. 
The Millennium 87db tweeter is old school. The wteeter i should have upgarded to was the Seas Exotic 94db sens tweeter for the same price.
I just didn't know much about how this sensitivity comes into play.
My guess, looking at the fq sens chart for the Exotic 8 woofer, the deeper bass fq's is just not there. The W18E001's , guessing, outperform the Exotic and the new Seas Graphene W18 no doubt outperforma sthe older Exel W18. 
Woofers rated lower than 90db is acceptable. 
Its in the midrange and highs where any driver under say 94db, will not perform on the same level as a 95+db *Full Range* speaker in mids.
From what I've heard the lows/highs tend to be rolled off in *Full Range* drivers. 
Which concurs with my testing of cheap chinese *FR* drivers, the highs are rolled off, the lows are not as solid and punchy as the Seas W18.
Bass can be had from any high quality higher end  7-8 inch SB Acoustics, Scan Speak, Seas. But  these woofers are pricey. + Your xovers will be expensive. 
I am getting ever so closer to designing my *final* speaker, The Frankenstein. 
The W18's will remain as bass, The Voxativ Ac1A for mids/ upper bass, and either the Magnovox tweeter horn with a  2.2 Mundorf cap or a  AMT Planar tweeter /just bought off ebay/ , arrives next week. Both in a shootout for ultra highs. 10k+fq.
I have no idea the fq range on the Voxativ, so hard to say  how The Frankenstein will evolve.
So yes to answer your Q, the very 1st spec i look at/consider is the sensitivty rating. 
With 100 watt/channel amplifier I really don't need the 97db, but since its avaliable at same price as Vox's 91db speaker, may as well help myself to the added 6db sens. 
Dome tweeters with under 90db rating, just can not compete with high sens FR in the lower mids through high mids + low highs 10k/under
Just can't. 
When you look at your dome tweeter in the speaker, its old technology  due to lower sens rating. You are missing alot of the nuances in the music. The wet blanket treatment.

Yes but you need to discuss the sound of the old technology dome tweeter vs tweeters of differing designs. Not to mention that the characteristics of exotic material drivers when driver beyond their comfort level can be a real problem which forces the designer's hand in terms of the crossover. You can feel that sensitivity is the single most important factor for you, but this is not gospel.

 but this is not gospel.

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This is what I am preaching, and no other doctrine/dogmas.
Sens is the most critical spec when considering midrange/tweeter fq's. 
There I re-adjusted my thesis. Excluding woofers, as my W18E001's are 87db yet still remain one of the finest sounding bass speakers. AS we know FR has some issues with rolloff in the low bass region. 
Voxativ calims their FR drivers go into the 20hz zone, but from what i am hearing , added bass is needed. 
I have no idea how low the W18E001's go now, with the Mundorf Supreme caps,  the bass reproduction  on kettle drums in my classical music is rich, tight , just wonderful. 
Note the 20hz-30hz,  not much in classical music in that fq range. Maybe jazz fans need the 20-30hz, but in classical  its miniscule notes in this fq range.

Dome tweeters in my experience can  not match what a  higher sens horn tweeter can do. The shootout always goes to the horn. 
The AMT  planar tweeter arrives this week,  rated 97db, We will see how this shootout goes. 

The higher  sensitivity = the superior  speaker.
(excluding the massive compression horns which are not meant for high fidelity home stereo)