> A single edit with the goal of ruthlessly eliminating every unnecessary word

This phrasing makes it clear that the goal of that edit is to eliminate every unnecessary words.

> A single edit, eliminating unnecessary words

This phrasing implies that just one edit is needed, no particular focus, and is satisfied by eliminating some unnecessary words.

> This phrasing makes it clear that the goal of that edit is to eliminate every unnecessary words.

By your own interpretation, we can get rid of "ruthlessly", no?

> This phrasing implies that just one edit is needed

I don't think it does, even when disconnected from the rest of the sentence. It's fairly clear to me that it's talking about an edit where you "eliminat[e] unnecessary words" which may or may not be part of a greater editing process.

Eliminating unnecessary words works wonders.

I don't agree that those are unnecessary - you lose the idea of an idea, and coming back to a work later can help you identify what is unnecessary.

Neccesary words? Wonderful!

Why use many word when few word do trick?