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I think most of the issues you point to here would be readily apparent to any seasoned audiophile without the use of tools. All but the crossover. I am not exactly sure what a leaking cap would do. But a Blown tweeter, or fuse. Very apparent. Out of phase or channel reversed. Anyone who spent 10 minutes checking these would hear it and get it right.
IMO, its the room speaker interactions that are not as apparent that tools reveal. The more subtle dips and peaks. I'm not sure about the compression of soundstage or the size of the sweet spot. Do tools measure for this?
But then the can of worms is opened. Does a microphone and computer software give answers. What if it says you have a 6db suck out at 100 herts. Does the software say, set a subwoofer here in the room, adjust the phase, intensity and crossover to these settings and it will go up by 5db. Does it say pull your speakers forward/backward 1.5" and out/in 2". Or are you left staring at your tool thinking, my system sucks!!! What can I do. Hmmm, maybe new speakers will solve the issue
I think tools are excellent. But just because you bought a chisel does not make you a carpenter. I would have no idea what to do with the data. I would only be able to randomly start moving stuff around. Maybe if I spent some amount of weeks on more specific forums focused on software analysis and room speaker interactions might I start to untangle the web in a more "scientific" manner. But I believe it would be a long road of trial and error. If that were something a person had the time and inclination to engage in, then more power to you. In the end I would say that person is going to get a better result than the one who only goes by ear. So I agree with you. But I also throw caution as I don't believe it is as simple as some appear to make it be.