What are we objectivists missing?

You mention cables,  if 2 measure "exactly " the same then they will be indistinguishable in an ABX test. The reason people claim they hear differences in components that measure the same is due to confirmation bias. 

Another possibility:

The new cable is different in length, gauge, or termination than the old cable.  So it brings slightly higher gain to the system, which some users perceive as improved SQ.  

My take is that if you can hear a difference, there must be some difference.  If a device or cable or whatever measures exactly the same it should sound exactly the same.

Can you measure brain and soul? I believe you cannot even measure your ears fully.

Colours have shades too, they are not only come in red, blue, green, etc.

Do all people see the same colouring, do all people have the same sensitivity to light? I do not think so, no bias here.

But i do agree that it is a hobby so no big harm.

I would like to see a complete set of new measurement method by the people who do that, till then enjoy.

What is the problem you are trying to solve?

Is this about aligning measurements with certain auditory outcomes?

Measurements can indicate the performance relative to the parameter being measured but cannot (by themselves) accurately predict a subjective outcome, such as which cable (or electronics, or speakers, etc.) that somebody will like best.

Measurements have been getting better but they are still imperfect.  Aggregate measurements of complex systems (the whole) are not necessarily fully reflective of the parts. One can measure down to component level and see differences which don't necessarily get reflected in the overall summative measurement. In addition, measuring dynamic phenomena in complex systems is even more complex e.g. weather forecasting and macroeconomic modelling (and reproducing music).

If we knew what the missing measurement parameters were, we'd be using them and they'd no longer be missing.