To be fair to the idea, it would work out just fine if just a single spacefaring species evolved, discovered their piece of the puzzle and then sought out the others.
I do concede that it is really unlikely that they would all evolve on all puzzle planets at roughly the same time and all be spacefaring around the same time. But I guess that’s why it’s a plot device to bring them all together and kinda explain why everyone is human with weird eyebrows, ears or noses.