There is a difference between living a long time and living forever (being eternal). If you live forever then it is almost impossible there would be something you don't do, whether that be betray someone or even eat a food you don't like. The possibilities are shoved against it.
Except is been implied that Paarthurnax is getting older and eventually, dies either by old age or some dragonslayer. Even then, its more he have alot of life left to live rather then living eternally. He is not going to switch to rogue in the future if he practically spend the past thousands of years of teaching the Way of the Voice. He would most likely spent his remaining years trying to get the other dragons to be in peace with themselves and not get stuck on rage mode.
Besides, most of the liches you mentioned (if not all of them? Certaintly the underking and Barlizar) are now dead, so you cannot say what they would of done if they really did exsist for an eternity.
And if they were to live, they would most likely to continue doing what they were doing, being guardians of an item or the Empire.
One other thing, when you killed alduin in the MQ you did not absorb his soul, so you didn't really kill him. When you inquire about it, Arngeir would mention it to you, saying that Perhaps Alduin was not truely defeated, and he is destined to return and finally destroy Nirn.
Alduin is a special case ie mantler of the Time God of the end. In other words, he is not a normal dragon. Even the Greybeard mention this with comparison with you being special compare to all other mortal at teh end of teh game when ya mention ya defeated Alduin. Hell, all PC in any TES game are special in a way that no other mortal can achieve.
And there is more then one way to end the world and right now, the Thalmors are aiming at destroying the remaining Towers that hold Mundus together, one of these tower being the Throat of the World/High Hrothgar. Guess who live there and be its guardian when the Thalmors want to destroy it.