Should Speaker Manufactures provide a Frequency Response Graph?

“It merely requires an understanding of how the measurements correlate to perceived should quality“

Good luck with that.  A panel of listeners will rarely, if ever unanimously agree on the sound quality of a speaker or system.  On top of that, any speaker will sound different based on the room, the setup, the amps, the cables, the source, condition of the power coming into the system, etc.

“…take any two tweeters and provide a CSD/waterfall graph for each.  Based on the graphs, I could tell you with certainty…“. No, not with certainty.  You might guess right some of the time.

“… a speaker with a wider horizontal dispersion over a large bandwidth will produce a bigger soundstage than one with a narrower dispersion over the same bandwidth.“. Not really.  Careful, you are using lots of fancy terms here without context.

Have you actually designed and built a speaker?

@mijostyn 

”The amplitude response of a speaker is a moving target. It will change depending on the room. There are also other factors that play a significant role in audio fidelity like phase behavior and group delays. I do not pay attention to specs. I review the design of the speaker and make the best determination I can that I will be able to make the speaker perform to my expectations.”

“I might also add that measuring your system in place is much more informative.”

This is how I roll. However, when I was much younger, I was a technical specification person. If the device had low THD/IMD and depicted a ruler flat response, to me, it must be a good thing. As we grow and mature in this hobby, we now know through experience that that methodology is not entirely accurate as to what we actually perceive as musicality in the actual operating environment which has numerous variables. 
 

There is one caveat. When auditioning very large speakers, multiple listening samplings at various locations / venues must be conducted in order to grasp the persona of that speaker. When comparing and contrasting a speaker you have owned for many years to something different, it will be readily obvious that what you hear is either good or bad in a fairly short amount of time. That’s why when I go to audio shows and walk into a room, if it sounds bad to me, I am out in either a few seconds or a minute. My comparative reference is different than anyone else and what sounds good to me, may not necessarily sound good to someone else. 
 

What should start a new thread call titling it “What have you learned” or something like that. 

For what reason?  Are you going to buy because of the chart?

Great question @bigkidz ....The chart is more likely to cause me to avoid a particular speaker. If for example the speaker has a rising response due to lack of baffle step compensation....that's not for me. I know that speaker will sound too forward and possibly even shouty.

So if they or ASR wants to post frequency curves that's fine, neither will tell me what they measure in my room.  

@sunshdw Your speakers will dominate the measurements until the room starts to take over. If you have a larger room, the room will start to dominate the response at around 500hz....for a small room it's around 250hz...

However, if you have a very small room or speakers very close to sidewalls for example, you're going to end up with phase cancellations or peaks at much higher frequencies. 

Lets say a speaker has a 5dB frequency response error due to a rising response...and then your small room is reinforcing that peak another 5dB...at that point a 10dB peak in the mids or higher frequencies will make the speaker unlistenable...this is a core argument for mitigating frequency response errors at the factory.  

@seanheis1 It is rare now for speakers to have a 5 dB anechoic amplitude error except at the very ends of the audio spectrum. On the other hand early room reflections can cause errors over 10 dB. I had a window adjacent to the right channel speaker I had to remove because of a 12 dB response error it caused above 10 kHz. 

Amplitude errors do not just occur in the bass. They are usually more pronounced in the bass, but if anything in the room is resonating, like my window, strange things can and do happen. Using "room control" only in the bass is inadequate. It has to cover the entire audio band. When a processor can perform room control an added benefit is that it can also do EQ given the user the ability to voice their system the way they want it.

I want to also add that the knowledge of what an audio system is or should be capable of is gained only by experience. You have to have heard a system performing at that level. Live performances can be useful, but only if acoustic in nature. Once you add amplification, particularly in large venues, all bets are off. The sound quality at large stadium concerts is typically hideous and in mono. A good system with a good live recording has no problem outperforming that circumstance. IMHE, as an audio insider in the late 70's and 80s, experienced listeners always know when they are in the presence of an exceptional system. It only takes 30 seconds of a familiar recording, you can see their eyes widen, and exceptional systems will do this to every honest experience listener that hears them. Not that these systems have no faults, their faults can be glaringly obvious, usually in the low bass, but their performance extremely convincing none the less.