The faint hope is that people are not crazy or suicidal enough to build a world-ending technology, that humanity will manage to see ourselves as being in the same boat, where we all live or all die as one. And just-not-do the thing that causes our extinction.
It's not a very realistic proposition, because even smart people often fail to understand these arguments (or just disagree with them), let alone the politicians (who are incentivized to ignore them), or the rest of the people. There's a lot at stake for the "winner" of the AGI race, who could build an AGI and align it successfully (which they can't do). And many countries are ruled by people who are clearly willing to do crazy and suicidal things for power.
That's why the author of this post doesn't put a lot of hope into the idea of his daughter growing up.
I also don't think it's that likely that a leader would take those odds, if they understand the risk fully. The worry is that they won't understand or believe the risk, so that's where we should attack the problem, in my opinion--by putting out as much good information on AI risk, and combating misinformation, as best we can.