How do you know that your character is the last dragonborn? Akatosh is what? A duck? No. A witch? No. A dragon! Right! Alduin is a child of Akatosh. Akatosh "gave the gift" of dragon blood to St. Alessia (the book doesn't say exactly HOW, but from reading Norse and Greek mythology I can guess pretty well -- gods used to leave their planes of existence to impregnate women), and thus established the dovahkiin. One of your character's ancestors is a descendant of St. Alessia and Akatosh. It's the only way. Your character carries the dovahkiin genetics. (S)He will pass them onto their children. Apparently they can lay dormant for decades and then express themselves when needed. So the gene will probably express itself at some point in the future again.
When misrule takes its place at the eight corners of the world
When the Brass Tower walks and Time is reshaped
When the thrice-blessed fail and the Red Tower trembles
When the Dragonborn Ruler loses his throne, and the White Tower falls
When the Snow Tower lies sundered, kingless, bleeding
The World-Eater wakes, and the Wheel turns upon
the Last Dragonborn.
Your character could not absorb the soul or Alduin. Why? Because Alduin will return when Akatosh sends him to end the world. Singling out Paarthurnax for death makes no sense. No character who has gone through this entire game has earned the right to pass judgement, especially if they have done the Thieves Guild or DB quest lines. Even the Companion quest line is suspect.
First off, it's Alduin's destiny to end the world. It has to happen eventually, nothing can change that. However, he isn't supposed to control the world as some dragon god. Secondly, Paarthurnax is the second strongest dragon effectively making him the closest thing to a new dragon king.
And so Paarthurnax decides he wants to be king of the dragons? He has to get them to follow him first. That is going to be more difficult than he thinks. And if he does? So what? Someone needs to be in charge.
Not that difficult. Dragons respect only power. They will follow the most powerful dragon until they doubt his ability, Odahviing tells you as much. And no, nobody needs to be in charge, all dragons have to die. Dragons aren't like mortals. They don't think the same way or feel the same way. They are closer to Daedra.
So before you pass judgement, I ask you to look at your statistics. Look at the number of people your character has killed. Look at the number of murders. Forget the bounty. That just means someone saw. Look at how many game days have passed.
It's not about morals or judgement. If I didn';t believe in redemption, I would';ve killed Erandur but he's my favourite follower. It's about dragon nature and risk. There isn't anything that proves Paarthurnax's ability to restrain his dragon nature- after Alduin's defeat- for the rest of his immortal life.