Speaker priority: high or low???

Yes, David, you are right. The speaker cannot "improve" the signal presented to it. As I understand it, what Karls, Unsound and others have said (more ably than I) is that the speaker is the component that is least linear and most apt to impart its "sonic signature." There are clearly demonstrable, relatively gross (objectively and subjectively) differences between speakers. There are not such gross, subjectively and objectively demonstrable differences, for example, between a $500 CD player and a $2,000 CD player. A pair of AR3s is going to sound like a pair of AR3s with $20,000 worth of electronics and will sound like a pair of AR3s with $1,000 worth of electronics. --- The identifiable "quadness" of a pair of ELS 57s will remain regardless of the electronics. A bad amp may muddy the midbass, and present unacceptable colorations to the revealing midrange of the quad. And to be a bit hyperbolic: a deaf man would not mistake the AR3s for the Quads regardless of the electronics used with either or both.

Speakers are much more than "tone controls". They are the imperfect acoustic interface for all the "upstream" components. They are electrical-mechanical transducers with high mass and relatively large nonlinearities and other distortions compared to the electronic components in the system. Even with relatively "low-fi" electronic components, speakers are usually the most limiting factor in an audio system. Consequently, only with better speakers can you take fuller advantage of upgrades made elsewhere in the system.

Now, I am just a fat little boy who works for a cheese company, but in my experience, I can live (and sometimes quite well) with lesser speakers, if they are driven with better electronics. The reverse is not true. My main system is posted. I have swapped out my main speakers (5 driver tri-wired) for Warfdale Diamond 6's (2 way, single run, $149 a pair)(I admit, they have been modified). Once they were setup properly, the Warfdale speaker gave me most of what the main speakers do, with the exception of the lower registers.
If the truth be known, I fall into the Beemer camp of balanced systems, but I am willing to play. I would be much more inclined to live with speakers that were designed with some trade-offs and no glaring errors, as opposed to something better that revealed more of the trade-offs up-stream.
Again, this is just me.

Speakers come first. Then tweak / upgrade the sound with better amplifier.

Of course you can't take this too far because ultra-revealing speakers will show upstream component's faults.

Amplification is hard to explain. The differences are subtle but bad amplification can be very wearing over time.

I never considered the "Speakers are the most important because they are the most flawed" philosophy. There is merit to this.

Squidboyw (Is he really fat?) throws the interesting spanner into the works. Comments like this have been made in the past. Is it possible they are without merit? I did not hear his experiment so I cannot comment with any credibility about the results. If he really heard that level of quality from his admittedly modified Wharfdale Diamonds what does this say about our pursuit of the perfect speaker?

I have long had the opinion that in a balanced system the speakers are the least important componant. This is obviously not to say that speakers are not important. There is no sound without them, although there is no sound without any other componant. I may have to rethink my conclusion but I doubt I will change my mind.

I'm am not an engineer so I actually know little about speaker design. Is it really that hard to design a speaker without major flaws and compromises? Just like amplifiers, there are so many designs and philosophies behind the speakers. Stereophile commented several years ago when when two very popular amplifiers of extremely different design came out that "If one these amplifiers is right than the other must be wrong." The problem was they both sounded great to their reviewer. I think they were a Krell and a Jolida, not that it matters.

So anyway should speakers be moved up on the list of priorities or are they where they should be?