The Flash's ability to time travel using his speed has always been a problem, but it's actually more than just that. When analyzed fully, it's really an existential nightmare for the entire DC Universe. A perfect example of this is in the DC altering crossover event Flashpoint. The series was written by Geoff Johns and illustrated by Andy Kubert.
Most every comic fan is fully aware of what Flashpoint is and the catastrophic effects it had on the DC Universe. For years, Flash had toiled with the idea of going back in time and saving his mother from his nemesis the Reverse-Flash. When he finally does it, however, the world is changed for the worst. Aquaman and Wonder Woman are at war. Superman was locked away. Most notably though, Bruce Wayne was dead and the Batman mantle was in the hands of his father Thomas.
The story of the crossover itself revolves around the Flash as he tries to come to with what happened. He doesn't have his powers, but what's even more striking is that he doesn't understand how the universe became so twisted. He believes it was Reverse-Flash that did this, but he soon realizes that it was his own selfish actions that created the Flashpoint. He did so by saving his own mother, negating his origin story and completing erasing all memories of who he was.
The fact Barry Allen doesn't immediately how the universe was changed is a nightmare scenario for everyone in the DC Universe, heroes and normal people alike. It would stand to reason that everyone outside of Barry Allen would not their original universe, but if even speedsters aren't immune to the memory wiping then it creates a dangerous situation. If Barry died, or if his memory was wiped completely, then no one would have any recollection of the original timeline. Taking this scenario to its extreme, it's possible that speedsters and time travelers have been altering the timeline for years, unbeknownst to everyone.
Because Flashpoint eliminated the event that caused Flashpoint to exist in the first place, this reality-altering ability is paradox-proof. This is a completely nightmare scenario for someone like Batman, knowing that there are actually villains who have this power as well. Batman himself had a "Flashpoint-like" event when Booster Gold traveled back in time to save Bruce Wayne's parents as a gift. Of course, Booster Gold isn't a villain and merely created this alternate timeline out of irresponsible benevolence. Still, it could have turned out that Batman's and the Flash's "changed timelines" were for the the better. That's a terrible abuse of power that even the Flash wouldn't be able to resist.
