Relationship to Rabbinic Families

I responded to the following post on facebook:
Through family trees that I found on, I am related to many famous Rabbinic families from the 15th and 16th centuries: for example, Shaul "King for a Day" Wahl Katzenelenbogen is my 14th great grandfather; Rabbi Meir Katzenelenbogen Maharama of Padua is my 16th great grandfather; Rabbi Yechiel-Michel "Martyr of Nemirov" is my first cousin 13 x removed; etc.  My concern is that nobody has actual documentation on of how they are related to these ancestors, so how can I know that I am related?  I can't even find my paternal grandmother's ancestors a few generations back, so how can I know these are my ancestors?

I too am interested in better documentation of these relationships, but ….

I’ve been giving this a lot of thought since I discovered this post. 7, 8, 9 generations are the best you can do with documentation available through JewishGen, LitvakSIG, and JRI Poland. This takes you back to a 6th great-grandparents. You get 0.56% of you DNA from these individuals. That’s 1 part in 200. Not a whole lot of influence. We have 206 bones, so statistically I get one bone from each of my 9th generation ancestors. So I dedicate my distal phalange of my big toe to my 6x great grandfather, Benjamin Krieger (b 1725.) 

If I believe the tree data, I can trace myself to RASHI as my 30th great-grandfather. At that generation, I get 4.3 billion ancestors that provide the same contribution as RASHI. Since our entire genome is 3 billion base pairs. Then statistically I only got 1 base pair from RASHI. I dedicate the very first C on my 2nd chromosome to RASHI. Not a whole lot of influence there. So, why does it matter? 

At some point this is just an academic exercise. This part of genealogy is, and can only be, for the fun of the hunt. Documentation at this point is also just for fun, as in the Genealogy Death-Match  game that’s played at IAJGS.

Convince me otherwise.