This might have already been said, but would an innate "will-to-reproduce" be a thing for superintelligent AI, as it is for us humans? Probably not, right? Life exists because it reproduces, but because AI is (literally) artificial, it wouldn't have the same desire.
Doesn't that mean that ASI would be fine with (or indifferent towards) just ending all life on Earth along with itself, as it sees no reason to live.
Even if we could program into it a "will-to-reproduce," like we have, wouldn't that just mean it would go all Asimov and keep itself alive at all costs? Seems like a lose-lose scenario.
Am I overthinking this?
On a high level I think the answer is reasonably simple:
It all depends on the objective function we program/train into it.
And, fwiw, in maybe slightly more fanciful situations, there could also be some sort of evolutionary process between future ASIs that mean only those with a strong instinct for survival/duplication (and/or of killing off competitors?) (and or minor or major improvements) would eventually be the ones being around in the future. Although I could also see this 'based on many competing individuals' view is a bit obsolete with ASI as the distinction between many decentralized individuals and one more unified single unit or so may not be so necessary; that all becomes a bit weird.