This isn't how you are programmed to work.
Biologically nothing makes any sense. I mean this in the full nihilistic sense, nothing matters to cells and DNA and enzymes, they just follow the rules of physics and chemistry and nothing is better or worse, it's just a bunch of atoms bumping together.
However, evolution has programmed you to care *a whole lot* about your own children, and their children, and so on (but really it's just words past grand children for the most part, there is no biological programming to care about your 125,000 35th generation grandchildren, how could there be)
But then the beauty of the emergent behavior comes in, caring doesn't have to be global, because it is inductive. You care about your children, and they care about theirs, and so on down the line. Everyone is cared for, nobody has to manage to care about all the unborn generations to do a good job of ensuring their progeny will be among them.
This is also where people like Hawking aren't going to make a lot of headway, since we aren't really programmed to automatically feel anxiety about risks to the future of our race. Quick experiment (sorry in advance): Imagine the last ship of humans on it's way to Alpha Centari, the last hope of all of humanity; now imagine it exploding. Now imagine your kid on their way to school tomorrow, and a guy pulls up to them in a van and tells them he needs them to come help find his puppy. Which one made you feel really worried (assuming you have kids)? Now, it turns out he really did lose his puppy, but your kid does the right thing and runs into the school and tells a teacher. There, I let you off the hook, but if you are anything like me, just the thought of someone approaching my child makes me very anxious, but imaging humanity being wiped out in the distant future is the fodder of feel good sci-fi romps.