First, a caveat: I do occasionally read reviews on ASR, and would argue that Amir does, at times, provide interesting and valuable insights.
Having gotten that out of the way, here are a couple of thoughts on the matter.
The painting of both ASR or Audiogon contributors with a broad brush is ridiculous. There are at least some perfectly reasonable members of both sites, who neither over-emphasize the importance of measurements, nor subjective experiences, at least to any extreme degree.
No component produces music in a vacuum, and none will sound the same with every possible permutation of associated components, and listening spaces. So even if an amplifier, to use one example, were to measure exceedingly well, could Amir, or any other rigid objectivist, describe its sound signature without listening to it? They might argue that it is "neutral", and that any "signature", or changes in sound, would be related to other components in the chain. But even if that were true, everyone understands that some amplifiers pair better with some speakers than others, and I doubt very much that such synergy could always be accurately predicted based on measurements alone.
I use the above example, and could produce others, to help illustrate that listening is required in order to fully assess the performance of components. Synergy cannot be measured, and listening spaces can radically change the sound produced even by components that measure exceptionally well.
It is, of course, possible to predict some likely characteristics of amps or speakers, based on measurements. But for the same reason that no designer of such components would ever put them into production without extensive listening sessions, it is simply not possible to know how a component will sound based on measurements alone. And that, I would argue, is the slippery slope that the extreme objectivists try to avoid at all costs.