Ea-nasir Gambit
This temporal trick is the Time Patrol’s equivalent of an emergency field dressing, in the sense that it’s kept in reserve for use during a genuinely life-threatening situation. It’s not a desperation play; the Ea-nasir Gambit works perfectly well, which is why the Time Patrol uses it. It’s just that the Gambit is not a permanent fix. It’s barely a temporary one.
The math that explains how the Ea-nasir Gambit works is complex — to the point where parts of it have applied for, and gotten, official legal status as sapient entities — but the incredibly dumbed-down explanation involves temporal inertia. To put it obscenely simply, the universe is expected to go from Point A to Point B, and it does. Everything in between can be changed, but not permanently, or more accurately, it doesn’t matter if things ‘change’ or not. When the Big Crunch happens in the end, it’s not going to make any difference if Earth was the center of a giant stellar empire, or whether it got saved from being vaporized in 2145 AD, or whether the Union won the Civil War, or whether somebody turned left instead of right on the corner and thus discovered a really nice restaurant that she totally didn’t know was there. It all smooths out in the end.