Is this ‘not’ phrase o.k.?

You only become a legend by winning, not by giving up.

Is this correctly expanded, because generally when words are omitted to create an elliptical clause (in this case a ‘not’ phrase), the omitted words are taken from the preceding clause. But in this case, ‘do’ has to appear from thin air?

You become a legend by winning. You do not become a legend by giving up.

Or is it this, which means that the ‘do’ is no longer there?

You only become a legend by winning, and you only become a legend not by giving up.

Separate Question: Do you think that elliptical clauses should only be used in informal writing, and formal writing should have EVERY word spelled out, even NO compound predicates?

Thanks a lot. Understanding these elliptical clauses will really help me.

Is this ‘not’ phrase o.k.? You only become a legend by winning, not by giving up.

Not a thing wrong with it.

You become a legend by winning. You do not become a legend by giving up.

Is this correctly expanded, because generally when words are omitted to create an elliptical clause (in this case a ‘not’ phrase), the omitted words are taken from the preceding clause. But in this case, ‘do’ has to appear from thin air?

Do is standard with a negative sentence. (I like ice cream. I do not like ice cream.) Adding the necessary word do has nothing to do with ellipticals. The addition of do and the elimination of the other words are simply happening at the same time.

You only become a legend by winning, and you only become a legend not by giving up.

This sentence makes no sense (and therefore demonstrates the need to ellipticals.

Separate Question: Do you think that elliptical clauses should only be used in informal writing, and formal writing should have EVERY word spelled out, even NO compound predicates?

No. Elliptical are good rhetorical devices. They aren’t used informally. They’re used for effect—and to avoid repetition.