^ Yeah, the generation ship would have to be nothing but frozen embryos, because no group of people can be cooped up that long and not go nuts, and since the first or second generation would realize that it's 20 or 30 years back to Earth, and 4000 years if they don't turn around, they'll turn around, or at least stop (if reaction mass is only sufficient for one start and one stop), radio back, and await rescue.
The reason is that the early generation of people will look around and realize that for 4,000 years they can't expand. They can't really modify much. They can't go anywhere, they just exist. Their only purpose is to reproduce, die, and get recycled. Their children's only purpose is the same, ad naseum. It's too much for a human to face day in and day out, especially human parents.
Very good, I realized much the same myself, the fact that it travels through space is only incidental, its main purpose is to travel through time, and setting it on a journey to Alpha Centauri forces it to wait 4100 years, it could instead go in a wide orbit around the Sun for 4100 years, but then it could always come back early, going on a one-way journey to the nearest star commits it to leap 4100 years into the future, in case humans have technologically evolved into something inhuman, become drones or somehow destroyed themselves. We wouldn't want the ship's occupants rejoining humanity just in time for their destruction, at least if they skipped ahead 4100 years they may at least get a chance to see the peril and possibly prepare for it themselves.