If divine interventions (and thus miracles) are allowed, then the time and position at which they happen become distinguished, hence violating the laws of physics (if it were not, then it wouldn't be extra-natural, and could therefore be interpreted as part of "normal" life supposedly explainable by science). Thus, it would break the invariance of the laws of physics by time and space translation (no preserved energy or momentum, not even locally), and consequently distinguish both a point in space-time from any others, and a frame where the events happen at rest. It would also introduce a new form of dynamics and change: acausality, which is pretty scary.
In this respect, it is either our belief that there is no privileged inertial frames in physics that is a misconception, either the believe that divine intervention seen as extra-natural events can occur.
Now, not everything is explainable by science (thus the distinction between what is extra-natural and what is not is ill-defined - think about consciousness and life), nor the absence of divine intervention is killing the concept of a transcending "god" (in a weakened sense), with absolute moral and so on (encoded into existence through consciousness, feelings, ...).
My belief is that atheism as a rejection of any form of "supreme authority*" transcending the individuals and belonging to a deeper level of existence is much more naive than our usual religions. The success of science actually offers a much stronger objection to atheism and nihilism than it rejects the existence of some weaken form of god. "A little science estranges men from God, but much science leads them back to Him"
* the laws of existence itself (of physics, of reasoning, ...) are like that, try jumping from the 10th floor and see if you don't crash yourself on the ground.