fjn, your scenario has been the heart of the argument for the Linn Sondek table since it's introduction in the early 70's. That it is the ability of a table, in fact all links in the hi-fi chain, to play music, not just make sound, that should be the basis for judging it's performance. That there are other tables that perhaps excel in purely sonic terms---tighter bass, more extended highs, etc---but none that "play" music as well. That makes reproduced music feel and move (temporally) the way live music does. Hardcore subjectivists even speak of a table's ability to express the "intent" of the musicians and singers. That's about as subjective as one can get!
There is no set of measurements that correlates with or predicts a tables ability in this regard; it can be discerned only by listening.