The law of small numbers in relation to ancestors

Hello Rabbi,
You gave examples of all kinds of "fathers" who give blessings, and if I understood correctly, you linked this to the law of small numbers. With your permission, I think your approach is irrational, and I will explain why. I would appreciate your comment.
The fact is that there are many "babas" where people wait in line to receive their blessings. People wait with a particular baba, while not necessarily with others. This is a reality. Who told you that this has no real connection to the blessings he gives?
Doesn't the fact that people from all over the world came to the Lubavitcher Rebbe provide some indication? You can call it a strong intuition, a kind of prophecy, or any other definition you like.
The same goes for Baba Sali. It seems that you tried to forcefully put the phenomenon into the category of the law of small numbers, but how do you know that this is the correct explanation?
Your approach, the rationalists, seems to ignore reality. When there is a widespread social phenomenon, like the blessings of Baba Sali or the Lubavitcher Rebbe, perhaps it is necessary to investigate and understand why so many people say they were saved in particularly unusual events.
Who determined that everything can be explained using the scientific tools that exist today? Who determined that healing must be done specifically through "classical" medicine? In your lessons, you tried to compare Baba's blessing to classical medicine, but those who turn to Baba do so precisely because they have despaired or have not found a solution within the framework of conventional medicine.
There are many people who have visited Baba Sali and told their stories. These are facts – exceptional cases that have occurred. Why did you conclude that it is just the “law of small numbers” and not something that has not yet been explained? As a rationalist, you have to prove it, not just assume it.
Best regards,
peace