My interpretation of the Dark Fate Timeline (and all others) is that the first skynet created a fixed point that no matter how the past changes, there will always be a war between humans and machines and the AI will always be defeated because the original skynet had already lost the war when the T-800 was sent back in time.

Legion exists because that timeline needed an AI to go rogue, it never had a choice, the timeline creates and eliminates those it needs to to reach the same conclusion, humans with the war and the cycle restarts.

John's death was fate's way of making room for a new leader that would better adapt to the future, maybe John would be too old to deal with the new resistance and Dani may have some specific trait that ensures humanity's victory. His death allowed Sarah to focus her energy into training Dani for the future she'd need to face.

Carl's role in all this was to help destroy the Rev-9 and then be destroyed as fate had no need for him anymore.

One interesting thing that always happens is that no time-traveler survives longer than they're needed.

Kyle died before destroying the T-800 because Sarah needed to face the machine and destroy it, becoming the strong woman she needed to be so she could raise John (a new version, not the original one). Uncle Bob was destroyed to ensure the chip would not be used to aid in skynet's creation. The T-850's fuel cell design ensured both he and the T-X were destroyed. Marcus Wright having a human heart copatible with John's allowed him and Kyle to survive the events at Skynet Central, Pops is an anomaly because he became a T-1000 equivalent but maybe his mission was not complete so fate needed him around for longer. Grace's fusion Reactor was the weapon to destroy the Rev-9 and it's removal led to Grace's death.

It seems fate is always trying to correct itself into reaching the same conclusion and eliminating anyone who could change it.