grammar - Difference and nuance between することはない and する必要はな い/する可能性はない

I understand the grammar point "Verb (Dictionary Form) + ことはない" can mean either "There is no need" or "There is no possibility" depending on context.

However, what are the differences? Are there any nuances which I should be aware of? Can they simply be interchanged in any circumstance?

"There is no need" example:

わざわざここに来る必要はない
vs
わざわざここに来ることはない

"There is no possibility" example:

今日の会議を忘れる可能性はない
vs
今日の会議を忘れることはない

Answer

When ことはない is used to mean “there is no need,” I think that the nuance is that it is not only unnecessary but also should be avoided. 必要はない on its face value just states that it is unnecessary. (I wrote “on its face value” because if someone chooses to say that something is unnecessary, it is often because he/she actually thinks that something should not be done. But the phrase 必要はない itself does not mean “should avoid.”)

When ことはない is used to mean “there is no possibility,” I am not aware of any difference in meaning from 可能性はない. 可能性はない sounds a little more explanatory and argumentative than ことはない because of the use of the word 可能性 which is semantically heavier than こと.