I'm not sure what's so confusing about it. Audio systems are a combination of mechanical devices that work together to reproduce that elusive thing called music. There are well-made devices and badly-made devices. There are devices that work well together and devices that don't. A Chevy Geo isn't going to give you the same driving experience as a Ferrari. A speaker with woolly, sluggish bass and misaligned drivers isn't going to convey the speed and accuracy of your drumming very well, is it? Likewise, an amp with poor transient response is going to fail to do that. I'm sure you don't need to be told that pace, rhythm and timing are essential qualities in a good musical performance, whether it's a Haydn trio or a Steely Dan song. I think "PRAT" is just a short-hand way of saying that a certain piece of audio equipment, or a combination of them, conveys those qualities (or the lack of them) effectively. (AFAIC, not all the system PRAT in the world can make "Jazz at the Pawnshop" sound like an Eddie Condon group.) I think it's also a shorthand way of saying that a system conveys the emotional qualities of a performance. A system doesn't have to do EVERYTHING perfectly--any system is going to have limitations of some sort--but if it conveys the essentials it can still provide more enjoyment than a far more expensive and unwieldy system that doesn't.
I've been in this hobby a long time too, and I've heard systems that DON'T convey the joy of music. And if you've ever spent any time building your own amps, preamps or speakers, it's not difficult to understand how easy it is to get it wrong.