Under this scenario, I would have to naturally imagine that the disasters prevented through time travel would be of a scale exceeding those that were not prevented and warranted the potential risks posed by time travel. Namely, disasters of a scale that would have completely wiped us out. I'm picturing time travelers manipulating events to prevent a full scale nuclear war, or ensuring that we would have the suitable defenses and/or contingency plans for an asteroid strike or cosmic ray burst directed at the Earth.
Honestly, if developed further, this could be the basic premise for a fairly interesting series of sci-fi stories. Such a series could feature an elite agency of time travelers dedicated to tending to humanity's history and the spacetime continuum alike, preventing only the true disasters that would have completely wiped us out and also mending any damage caused to the continuum by time-travel. (Or, if we adopted the theories involving alternative universes being constantly created: perhaps we would say that this agency is tending to their metaphorical garden to create a continuity that may not be ideal but is one in which humanity at least persists.) The first entry in the series would naturally follow a protagonist who discovers- and is subsequently recruited into- that agency, and would naturally feature a heated debate as to why some of disasters, like World War II, were not altered at all by the agency due to their risk analysis contrasting the scale of the disaster to the potential damage caused by time travel. We could even have this rookie over step his bounds and make the future even worse in his or her attempts to improve it, learning first-hand of the extreme care required in selecting the what and the how of altering the past.