That is not always true. It can persist longer at times. X chromosome for one instance. I also have many cousins who are 5, 6th, 7th cousins etc, that I know of through DNA, probably because our ancestors married cousins repeatedly.
My ThruLines on my family tree only go back 5 or 6 generations...mostly from late 1600’s to mid 1700’s. Nothing later in the lines. I have connections with many cousins...up to 7th-8th, but not many common ancestors that we share. And quite a few people on my cousin list either don’t have a family tree, or their tree is private. My father’s line is very short. My mother side goes on and on, with many connections I have a hard time believing...too many well-known names that it connects to. Ancestry.com is okay, but I’ve found many of the hints they provide, as well as the family trees they provide you in those hints, are wrong. I only started mine in June, and I’m no where finished with my tree. I’m hoping I live long enough to be able to go back through it all, and correct any errors that I know probably exist.