While Wesley and MacDonald offer useful and linear metaphors to help explain time travel, those are just introductions—literally Temporal Mechanics 101. Wes provides a better description when he describes the various timelines as a grand tapestry, one that can unravel as easily as a sweater.
Thus, he and the other Travelers hold the tapestry together by finding mistakes and other issues and fixing them. However, when the Temporal Cold War seen on Enterprise turned “hot,” the fallout overtaxed the Travelers, causing more holes than they could fix.
Much of the second half of Prodigy season two deals with Wes and the kids fighting to save their reality by fixing the hole left when they prevented Chakotay from sending off an unmanned Protostar. Their chief antagonists in these parts of the season are the Loom, trans-dimensional scavengers who devour the remnants of changed time (think Stephen King’s The Langoliers).
With the introduction of the Loom, and more explanation about the role of the Travelers, we finally have a clear picture of the other side of Trek time travel. Big events cause whole new timelines, but small events can either be devoured or fixed. Thus, Edith Keeler living would’ve either forced the Travelers to do what Kirk wouldn’t, or would have sent the Loom to descend on the former timeline, devouring what was left.
We’ve seen aspects of that already in Trek, most notably in the most recent season of Strange New Worlds. In the season two episode “Tomorrow and Tomorrow and Tomorrow,” Kirk and La’an meet Khan Noonien Singh as a child, long after he was to fight in the Eugenics Wars. A Romulan temporal agent they encounter expresses frustration at her inability to change the past. No matter how hard she tries, things don’t change, she complains. “It’s almost as if time itself is pushing back and events reinsert themselves and this whole thing was supposed to happen in 1992,” she vents.
At first, the Romulan’s complaint pointed to fallout from the Temporal Cold War, that Daniels/Kovich and other agents messed with the timeline so much that it has to change. However, Wesley’s explanation, and the introduction of the Loom, points to another. To save the timeline from being devoured by the Loom, the Travelers pushed things back into a different place, such as moving up Khan’s birth. The major event—Khan and the Eugenics Wars had to happen. But the Travelers had some wiggle room, allowing the Eugenics Wars and World War III to kinda become the same thing.