What situations is it necessary to exceed the speed limit?

When other cars do. This is why, regardless of any other rationale, we can’t automatically limit speed limits anywhere unless we can do it everywhere all at once.

Sometimes in passing a driver acting dangerously it pays to get passed them as quickly as possible.

Or perhaps getting away from a natural disaster.

You mean like a tornado? Most natural disasters will end up with many people clogging the roads, generally won't see a lot of speeding as an option.

An unintended consequence of this will be massive lines of cars going down the highway because no one will be able to get up the speed to pass safely.

Going well below speed limit for no reason is also illegal in _some_ places.

Once I was in a remote national park with a friend of mine, and they started having stroke-like symptoms.

We talked to the medic on site, and luckily the symptoms seemed to be abating. The medic (also a LEO), told me to drive my friend to the nearest hospital, 45 minutes away. The medic said, "Drive fast, but not too fast. Unless the symptoms get worse, in which case drive REALLY fast."

The symptoms did not get worse, gratefully. But this is a case where a LEO was telling me when it would be a good time to speed.