I know what you're trying to say, but your statement is wrong. Most extinct species died out without leaving descendants. Several major extinction events killed off roughly 90% of all species living at the time, and the earth was repopulated by the minority which survived. Most of the extinct hominids you talk about all the time left no descendants; only Homo sapiens survived.
All life on earth has a common ancestor
The term "species" is an old taxonomic designation. A whale is a species and dolphins are a different species. However, whales and dolphins can interbreed to produce "wolphins" A species is simply a snapshot of evolution in progress. Chihuahuas are the same species as great Danes. If we killed all of the other breeds and only had those two left, they would be separate species because they could not interbreed.
Even the extinct species that left no descendants were intermediate. They were just killed before they could speciate further.