Not at all — the farther one goes back, the more connections one finds, particularly to the first New England families who managed to survive. If you’re part of a surname organization, or one exists (”Smith Family of America” for generic example), often they offer some kind of genetic testing deal. That’s interesting in its own right. Turns out that people who, on paper, are all of common descent turn out to be split into groups, those groups being related internally to each other, common ancestry, but not related to any of the other groups. :’) I’ve not had the money to burn on that yet, but I know that is the situation among members of one of my family lines who have had the testing.
One quibble — “direct descent” is redundant, there’s no such thing as indirect descent. :’) I used to work with someone who was *related* to Abraham Lincoln, but instead claimed him as an ancestor. He has no living descendants. :’( I also used to work with someone claiming to be descended from Aaron Burr (through supposed illegitimate offspring), someone claiming to be descended from the Dalton Gang (presumably not the entire gang, so it was probably more of a cousins relationship, not ancestral), and there are old stories among family members that we’re descended from this or that historical person, but there’s zero evidence for it.
Given how Mark Antony behaved, probably half of Europe has him for an ancestor. :’D