“The hate of men will pass and dictators die. And the power they took from the people will return to the people. And so long as men die, liberty will never perish."

Similarly:

"Science progresses one funeral at a time".

https://en.m.wikipedia.org/wiki/Planck%27s_principle

"Give me liberty AND give me death"?

I'd prefer to solve the despot problem in a way that doesn't involve me getting dead.

Several countries have managed to not have despots for long periods.

Sounds like a self solving problem.

I reckon people will start caring about their despots if they expect to live a millennium under the despots' boot

I suspect people not caring is not the main underlying cause of despots.

Despots make sure the people who care are killed off (or at least marginalized, say in prison), leaving only people who don't.

I would not be so sure about that.

If you were expecting to live a much longer life, people might grow more fearful about the consequences of speaking up against a dictator.