Also at high altitudes, the exposure to the weather-related phenomenon is pretty less. Imagine a thunderstorm brewing up. No aircraft pilot would want to risk his plane getting stuck in such a weather. It is hazardous for the airplane, hence flying high also takes care of running into extreme weather situations.
The element of safety is also applicable to flying at high altitudes. Most of the modern aircraft are sophisticated pieces of equipment and they have the fail-safe mechanism for most of the issues that can crop up in flight. Provided the pilot has time in his hand to rectify the situation. He can only have ample time in his hand when he is flying at high altitudes and there is a window period between taking corrective measure and hitting the ground.