Ok, I think I figured it out and if I'm wrong I'm going to unsub permanently and uninstall FFXIV from my laptop (I will post videos of me uninstalling FFXIV).
Here it goes:
Hydaelyn was not summoned to shackle Zodiark. She was summoned to shackle Darkness / The Sound. In order to shackle Darkness she needed to sunder the star and Zodiark getting sundered is just part of the package. An unfortunately necessary side effect. Whenever Minfilia (in 3.2 after The Anti Tower) and Venat (in 5.2 after Anemnesis Anyder and again at the final cutscene of 5.55) talked about Darkness, they were not refering to Zodiark. They were refering to the Sound. Note that Venat said "Darkness comes", not "Zodiark comes".
Here's the proof:
First, Venat's group acknowledged that Zodiark was useful to stop the Sound. However, they recognized that this was not a permanent solution. The Sound will eventually defeat Zodiark and destroy the world. They tried to warn the convocation but were ignored.
This was also mentioned by Minfilia in the Anti Tower.
Note that she said "Darkness coveted power", not "Zodiark coveted power". But what about the first statement in that pic? Light and Dark did once dwell as one? I believe Light here actually refers to Zodiark! Zodiark was summoned to balance the Sound! Since the Sound was Darkness, Zodiark was Light! That's why Elidibus, as the heart of Zodiark, cares so much about balance. Because the essence of Zodiark is to balance Light and Darkness. And that's why Elidibus appeared as the Warrior of Light, because Zodiark was a being of Light! Unfortunately, Darkness is winning the battle and Zodiark is losing, which Venat's group realized.
What about when she said "I was forced to banish Him unto the distant heavens". Him here can refer to either the Sound of Zodiark but I believe it's Zodiark. She was forced to banish Him as a side effect of the sundering. She sundered the star to prevent Darkness / the Sound from getting stronger and unfortunately, Zodiark has to be sundered as well. She was forced to do it.
And note her face expression when she said Zodiark wanted to become whole and that the Ascians are working tirelessly to achieve this. It's an expression of sadness, not anger. She understood why the Ascians want to do it but she could not allow it because that means the Sound would be a threat once again.
Everytime a rejoining happens, Darkness / the Sound gets stronger. Note that she said "Darkness grown stronger" not "Zodiark grown stronger"
(continues below)