We cannot have them though? The leaders die and the resulting fights over succession is what keeps us out of eternal territory.

These maniacs didn’t have enough time to accrue enough mass to become power black holes, but give them a century or two to work with..

I don't know.. we have dinasties where direct ancestors of the ruler rules the country for generations, no?

That happened indeed and I don't think it was pretty. Although you get some exceptions, like maybe a few of the Antonines. (That didn't end well with Commodus.)

Nah, the fact that even emperors die is a good thing. No dynasty lasts forever, because after the first few generations, assets get diluted, someone spends the money, descendants fight, etc. An aristocracy that lives forever would be very hard to remove because those factors would be greatly mitigated.

Immortal emperors may produce shorter-lived dynasties, as it means no changing of the guard to provide the dynasty with fresh blood.

Rulers, set in their ways, will take a government down an increasingly non-viable path.