I'll tell you what makes me laugh - the notion that if two amplifiers measure the same and are 'audibly transparent', they must sound exactly the same and the only reason they won't is your own bias and preconceptions. Your hearing must be flawed, of course ...

I have been thinking of my recent experience with Loudspeakers, many well reviewed and measure well. All sounded different and only one I liked enough to purchase. I however believe other people would prefer a different presentation to me as my ears have a familiarity with the openness of open baffles and most people do not have this as a experience or preference. I have no idea how you measure for that kind of preference in sound and certainty even if you could I would have no idea what I was looking for. I do know what I hear for myself and understand my own pretences.

Back to the opening post question, I would say that measurements can help, or hinder, or just plain mislead. They need careful interpretation if they are to be truly helpful but in many (most) cases they just cannot provide any kind of indication as to how the component will sound.

This was encapsulated for me by a Facebook group I joined very briefly a few years ago. They professed to be about "just components, no foo". As soon as I started talking about a regenerator, the objectivists all went on the attack and the forum manager demanded to know what possible difference a regenerator could make because "all well designed power supplies can easily cope" blah, blah, we've heard it all repeated a hundred times before.

They wanted measurements, so I gave it back to them.  I asked "what measurement would you recommend that tells me what soundstage depth perception I can expect from a component?"  Well, that raised the blood pressure to boiling and they threatened to throw me out.  I quickly left.

Measurements don't adequately tell the whole story.