All these are important:

Avoiding contamination of water supplies. Let's face it, most of us don't go very far from the tent during middle-of-the-night outings.

Reducing impact on the banks of the water source, particularly lakes. The banks and shores get more than enough wear and tear from those seeking water and from anglers. Of course the more popular the area, the more important it is to camp well away from the shore.

Leaving the area near the water source free for wildlife to visit during the night. Many animals will go without rather than pass close to humans.

Spreading out the campers so that each can have more privacy. I try to get a quarter-mile away (if the terrrain permits) for this reason alone.

The safety issue is important with rivers and streams, probably not so much with lakes. However, watch your tent site--a supposedly level-looking site can turn into a lake, or at least a deep puddle, in heavy rain!

Other issues include avoiding bugs and avoiding areas of high humidity which can lead to considerable moisture condensation in your shelter. These aren't the reasons the 200 feet (or 100 feet in some areas) distance is required, but following this rule will certainly add to your own comfort.

Remember that "water sources" include boggy meadows as well--they eventually drain into the nearest stream or lake.

I've been in some situations in which I had to break some of the distance regulations due to the unavailability of tent sites. This has happened to me a few times in the bark beetle-killed forests in the Rockies, where camping under dead trees would be suicidal. If I have to do this, I consider the distance from water sources far more important than distance from the trail. You can usually get out of sight of the trail without having to go the whole 200 feet.