That's the idea introduced to us in Beyond Light. In past timelines that Elsie Bray experienced, we were corrupted by Darkness and the Traveler left Humanity. She has gone through countless iterations trying to find the right path forward, and it led to us destroying the Black Heart in Destiny 1, because the Black Heart was responsible for the corruption of Guardians, including the player Guardian, in previous timelines.
What is still a mystery is what caused Elsie Bray to experience her time loops. The fact that we are entering the Fate Saga, and they discussed the extradimensional nature of the Nine and how that allows them to interact with reality in a very different way in the Reveal Event, including powers over time, implies the Nine could be responsible for Elsie Bray's situation, creating the time-loop to preserve life in Sol until they find a timeline where the Sol System is preserved and we defeat the Witness.
Whilst this is possible, if I remember correctly Elsie would be cast back in the timeline whenever the Traveler was destroyed (I think this is in the Dark Future lore book). If correct, it would suggest that the Traveler has a hand in this, casting her back in its final moments.
I don't think that is the case. Looking further into it, it seems that Elsie is sent back to the same moment in time whenever she dies.
There is also the fact that, while the Traveler's domain is the physical world through The Light, manipulation of time might be outside of its influence. The Witness could tear windows into time with the Darkness, and Deepsight can allow one to manifest echoes and memories of the past.
However, neither Light nor Darkness seems responsible for Elsie's time-loop, and current signs from Edge of Fate imply the Nine are the actual cause.