There's three counter-arguments to this viewpoint, however.
The first is that we as fans provide the institutional memory that permeates the club - it's a feedback loop that stems from the stands, is amplified by the media and is then conveyed to the ears of the folks at the club. It matters - it's probably one of the only voices any fans in England have left in the running of their club, since any real input or power was taken away from them a long time ago.
So, that is definitely a way by which the current lot are infused with the memories of our past. Now, you might say that this necessitates the fans *forgetting* the past in order to get the players to do so as well, but that goes into the age-old question of whether the players need to inspire the fans to believe or the other way around. There's no easy answer to that. But, either way, there is a definite mechanism by which players learn the history of our club, and by doing so adopt its baggage.
The second is that ,even if the players are unaware of our baggage, our opponents definitely are. I can't put it any better than Chiellini did after Juve professionally, carelessly dispatched us with one burst of action. Quoting from the Guardian...
Our opponents *know* we tend to bottle it. They *know* that if they just keep us quiet, our mental demons will start emerging more and more as the game wears on. So it doesn't matter if our players are unaware - our opponents are aware, and they will use it to outdo us.
The third is that the same performances and the same choking in inopportune moments is still present - regardless of the changes in personnel, this team can (and does) still choke at the death when things are on the line. It happens less often, and that is tribute to how heroically Poch has tried to rebuild us....but in the end, we are still making the mistakes we made with different teams, in different eras, many years ago. Not as many, definitely. But they're still there. So surely the team is still afflicted by it, regardless of how we perceive it as fans.
Ultimately, we've been there as fans and we've seen these things happen far too often. But we're not the only ones seeing these things happen. Our opponents have seen them happen. The football world has seen them happen. And this will filter through to whichever sets of players we have, I think - one way or another.