Seems very naive to think that people who have access to immortality technology aren't going to have children, and if you're immortal of course you're not going to watch your children grow old and die, so you share it with them.

I leave it as an exercise for the reader to count out how many generations you need to run this until it's 'oops, all self-replicating individuals with broken off switches.'

Forced to find the courage or die trying to. And I really doubt that knowledge that their despot will eventually die has much effect on people's motivation to rebel as in most cases there is a clear line of succession. In many cases there isn't even a single despot to point to. This isn't even considering how such anti-aging technology would prevent despots' mental acuity from deteriorating as they aged - in fact they would probably grow sharper as they gained more experience so to speak. And aging/succession have almost always been one of the greatest destabilizers of a successful authoritarian regime.

People might be willing to give their known-to-be-finite lives in pursuit of the Greater Good, but the equation changes greatly when you're giving up an eternity for the chance of making things better. More of the population would be aged too, so I think it'd be a lot harder to find the kids that usually die in wars.

Especially true if it is the AIs that get us the immortality- it definitely won't be equally spread, and any incumbents have a massive advantage.

I think more people would settle for worse conditions to stay alive. Do you think you'd be more likely to revolt at 150yrs old when all your family and yourself can live extremely long to forever? Or do you think the threat of death by killing wouldn't be an issue?

You’re assuming that the immortality will be available to you, not just to the political elite and billionaires.