How much can be measured -- and how much cannot?

I'll admit the obvious: we can't know all that we don't know. In as much as we might not be able to know in entirety what a system will sound like from specs alone, we can still get an understanding of many of the sound attributes a system will have from specs. Not only can specs be a valuable tool in shortlisting components for consideration, we can also use them as a baseline to share an understanding of how a system comes to sound as it does. Despite what so much of the reviewing community does to create a mysticism of how audio gear comes to sound a certain way, let's not forget that audio gear is still an exercise in engineering. The experience derived from audio gear might be predominately subjective, but getting to that point might be predominantly objective. I doubt we could have a satisfaction with either without the other. IMO, being able to correlate one with the other is an ongoing quest that needs to vigorously pursued.

Tbg, I respectfully disagree. Things like frequency response and dBW just a couple of examples of measurements that can be important in regards to what we might expect to hear.

Tbg, how about an amplifier's dBW into impedance? Or the predictable roll off at frequency extremes when there's issues of impedance mismatch or capacitance issues? Antenna and tuner specs can often tell some how well they can receive certain stations at a given locations. Those are just a few examples.

Newbee, I couldn't agree more.

An understanding of measurements does more than just disqualify mismatched components. Some measurements will indicate specifically how those mismatched components will sound to some degree due to the them being mismatched, it's not just a matter of taste.
Some performance measurements will be more important to some than to others. For example, depending on ones location, a tuners ability to reject adjacent signals might be more important than overall sensitivity, and for others the reverse might be true. If one has to listen through static, everything else might be moot.
Let's not forget that some of today's measurements might be somewhat meaningless because they existed in the first place. There was a time, when not all gear "measured up" the same, but because of measurements they now do. It would be unwise to ignore measurements to the point that might happen again. I think we deserve more published measurements that can give us a better baseline correlation of audio components measurements and their sonic signatures. Perhaps published measurements of amplifiers propagation delays might be useful? How about more availability of harmonic distortions in frequency domain? FWIW, and though it doesn't necessarily exclude those that don't, I've never heard a speaker that publishes good measurements for either a good step response or clean square wave have anything but good imaging and sound stage.
Once again, measurements can be a valuable tool, but listening, though fickle, is more important...But, one doesn't need to choose between the two, both are more than the sum of their parts.
As to why the audio rags don't follow up on differences between subjective listening reviews and objective measuring, well, I suspect it's not in their best business interest. Let the buyer beware!:-)

TBG, you've already posted that you've found some speaker measurements helpful. I can't help but wonder if upon further examination, you might find some correlation between some other measurements and some sound characteristics.
I like your proposal, very much!
Again, I think dismissing all other measurements would be imprudent.