While I agree that everyone's system sounds discernibly different, I still think that analog systems, across the board, have their own sonic signature which is shared between them. This sonic signature is unmistakeable, and easy to discern. Same, of course, goes for digital systems. (same also goes for tube vs solid state amplification)
My experiences differ from yours. I've repeatedly witnessed how people get swept away by a good analog sound, and often exclaim how that LP sounds more present, more natural than the digitized version.
But then, if I play the digital version right after the LP track has finished, nine out of ten times people change their minds and say how they were wrong, and how the digital actual beats LP. Interesting...
I personally find digital to be more convincing on a quick switch, the immediate listen. Somehow the details in digital playback seem harsher, giving off the impression that it is more precise, more 'there'. In comparison, LPs sound laid back, effortless, not even trying.
But those impressions are usually deceptive. On repeat listening it gradually becomes clear how superior LPs actually sound. To me, the difference is like kissing a girl with full bodied lips that have been botoxed vs kissing a girl with naturally plump lips. Yes, maybe the botoxed girl has larger, more plump, more juicy lips, but the finer details in the sensation one gets when kissing naturally plump lips is much more subtle, and much more deeply satisfying.
And no, I'm not going to now go to the second base analogies