The objectively acceptable
Nope.
Right off the bat I can tell you that objectivity can't be applied to the decision of whether to kill someone. That is why the debate over the death penalty is without end.
she possess the knowledge to save the archdemons essence from the Grey wardens
This phrase makes no sense. Do you mean that she has kept the knowledge of how to save the Archdemon's essence from the Grey Wardens.
If so, how does this objectively means she should die?
she also know secrets of the order that she shouldn't know

So does he. Does Varel objectively deserve to die?
she was also blathering of necessary change for people in order to be free
, due to her own frustration she was sure what was best for others like one of those crazy blood mages,this is more than enough to want her dead.
First of all, having an opinion of how things would be better makes Morrigan no different from 100% of humanity. This does not make someone's death "objectively acceptable".
Second, Morrigan does not even perform actions that are harmful to others in order to create what she perceives as a better world unlike people like Anders or Corypheus. You are the one advocating the murder of someone who never even once raises her hand against the Warden or the Inquisitor.
First she outright lied to my warden during the Flemeth quest,i asked to her as for why she was sent and she lied and sent my warden which was in good faith to combat against Flemeth,she didn't revealed the truth of the ritual at the time an yet i asked as for why she was sent,she lied,she confess in WH that she lied.
She did not lie to the Warden when she requested his help in killing Flemeth.
The fact that she was aware that she was sent to give birth to a reborn Urthemiel does not necessarely exclude the possibility that she genuinely believed one of Flemeth's reasons for sending her away were so she could prepare her body transfer ritual in peace.
As Dragon Age Inquisition proves, Morrigan genuinely believed Flemeth was going to try to possess her.
At redcliffe she deserted after that she gave her words to help in combat the blight,first to Flemeth later to my warden in person during the search of the first grimoire located into the mage towers,she said that with the grimoire she would have been more useful to me against the blight and yet she didn't maintained those words i found the grimoire for her she din' help in ending the blight,i count this as an heavy betrayal
(i don't care to discuss this point with her fans, to me as well as to many players is a betrayal)
Yeah, well, when you make a thread on these forums, you are opening the topic for discussion.
So, let us see, by Redcliff, Morrigan had spent around a year, give or take, accompanying the Warden around, from the top of the mountains to the deepest pits, fighting Darkspawn, golems, soldiers, demons, Abominations, etc, never once doing anything to prevent the Warden from taking actions she personally disagreed with and, possibly, even forming her first friendship with or falling in love with Warden and, when she asks him/her for something that she strongly believes in, she is refused.
And you're angry that she walks away? I'm sorry that Morrigan has opinions of her own.
It's not like every other Companion can walk away or even try to kill you. Oh wait, yes they can.
And weren't you just arguing that keeping the knowledge of how to save the Archdemon's soul from the Wardens means she should die? If so, why are you not taking her offer?
She went too far also when she suggested to kill all the parents and the family of my warden (this make the revenge personal) for no factual reason, as well as all those mages in the tower for nothing more than her personal ideologies.
Don't you want to kill her for your personal ideologies?
sure my HoF would have continued to hunt her down fo the rest of her life.
Located her is easly since she wasn't hiding anywhere she was at the imperial corut and she was easy to locate.
And being protected by the most powerful person in Thedas, the freaking Empress of the most powerful Empire in Thedas.
For my Inquisitor who never cared about the elves and did not respected the temple of Mythal,never performed the rituals and wanted to allow Abelas to destroy the well of sorrow as she was sure that one way or the other she would have find another sources of informations to kill Corypheus or at least his dragon, who was already losing badly at that point.
Morrigan killed the elf and showed great insubordination and later
pretended
to have the well of sorrow,now i do not know who was who wrote that part of the story but i had a distinct impression that was a choice forced down to my throat,either be a slave or let the shrew to have more power without being allowed to use someone else for the well of sorrow or simply pollute the well in order to not allow Corypheus to gain it.
This was an act of insubordination worthy of death for my Inquisitor, yet she Morrigan was allowed again of plot armor and forced to be in the Altar of Mythal even if she was not the host of the well of sorrow.
As a player i want an option to finish her for good this time,without stupid plot armors that will force my protagonists
(like the Warden in Wh) to let her survive for no other reason than sake into making the story of this foolish npc super mages.
If my warden would have been allowed to finish her Abelas wouldn't have been dead now and the well of FLemeth would have been destroyed.
Ok, so, your Inquisitor wants to destroy the only known source of knowledge on how to defeat Corypheus.
Morrigan wants to save it.
Ergo, she is the one who should die because she did not went along with the plan of destroying the only resource we have and wing it afterwards?
Seems to me, Morrigan just saved the world.