unless you have reason to believe they are unique or somehow superior in some way to the rest of the population.

Ahah, no, no particular reason, to the contrary, they're not especially good, and I am in favor of eugenetics (applied to those who do not exist yet, not those who are already alive!).

But as a genetic machine, you "should" care deeply, for a very particular definition of "should" - simply because if you do not, and that turns out to have been genetically related, then yours will indeed die out.

Yes, I understand the argument, and that probably that's exactly what will happen. On the other side, I feel no special loss pondering that the human genetic pool in the future will be composed by this or that sequence of adenosine and citosine.

The spectre of death is greatly lessened when you think there is a good chance that things you love will live on after you, remembering, maybe forever.

I think that's a cognitive illusion, but I understand that it can generate positive emotions who are not an illusion, by any means.

I understand that having kids, as much as unethical I think it is (that is, mildly), still generates for the way that some are built, some very strong good emotions, and those are not at all unethical.
Everyone has to balance the two, I guess.