Is it? I'd imagine they all share many common ancestors, but that those common ancestors are probably shared by many others as well so it's not very unique.

30 generations back (a thousand years?) you have over a billion ancestors, which is way more people estimated to have lived at the time, meaning your family tree at that depth contains the same people over and over. Of course your ancestry probably isn't uniformly distributed across the globe, but without modeling it mathematically my guess is that if you go back ~3700 years to when Abraham ostensibly lived you can find multiple people that appear in the ancestry of virtually everyone from the Old World.

Anyway intuition can often be poor when dealing with large numbers so if anyone has concrete math or research to share I'd be interested in being proven wrong.

It is indefensible to make arguments of likelihoods without and understanding of context and priors. If I listed 1,000 people from around the world at random and claimed we all had a shared great^N grandfather (with N not so large at to be trivially true), I’d need some rather significant proof to back up at that claim, and barring that we could say it was unlikely to be true.

If on the other hand I consulted my family’s genealogical records that had been painstakingly maintained for generations, including only those matrilineal lines that are most solid to trace, and from that listed 1,000 folks who have the same grandfather, then my claim would not be very unlikely at all.

This case is much closer to the latter than the former.