What tests would you like all speaker reviewers to do for their reviews?

As for the original question by the OP, I think we all need to agree on the objective of what a speaker should do.

From what I read in textbooks before, the objective may be stated as, 'A speaker should reproduce the electrical signal received at it's inputs exactly, as a pressure variation output.' Obviously, we all know from experience that this does not happen exactly, with less accuracy as it does with respect to electronics (pre-amps, amps). So we need a test to show that the speaker output waveform is the same as the electrical waveform input to the speaker. 

Problem: what about the microphone used to test the speaker?... What is it's transfer function? What room do we test the speaker in? Etc.

We all know that measurement of a speaker is not so easy. I suggest we look at the work of Floyd Toole, et al., as guidance for further discussion and work.

I would like to see them play different varieties of music for a change.

Spinorama 2034, near field driver, early reflections, in room response,  beamwidth,  horizontal and vertical directivity, waterfall , distortion @96dbspl, fundamental and harmonic distortion, maybe some 360° vertical and horizontal polars. 

Spinorama 2034, near field driver, early reflections, in room response, beamwidth, horizontal and vertical directivity, waterfall , distortion @96dbspl, fundamental and harmonic distortion, maybe some 360° vertical and horizontal polars.

most of those are the same thing with different names

Jesus dude go away you have no clue they each tell you something different. One shows FR on and off axis, port resonance and woofer resonance, others floor and ceiling bounce, etc.. it’s mostly all from using a Klippel, but each gives you different info.