'crucial consequence' is correct and usable in written English.
You can use it to refer to a very important consequence of a particular action. For example: "The failure to pass this legislation had a crucial consequence - price instability in the markets."
Another crucial consequence is the so-called urban explosion.
Her failure to do so had a crucial consequence: she made the wrong decision".
But the crucial consequence of the production's modernity is that it puts Iago at the heart of the play.
One crucial consequence of the Irish ballot may be its impact on people in the applicant countries, who must also vote in referendums expected next year.
One crucial consequence — the abuse of prisoners at Abu Ghraib — receives a single page (most of which is about Bush's reasons for not firing Defense Secretary Donald Rumsfeld).
But the crucial consequence of the voyages of exploration was the migration of foods from one continent to another, the subject of Fernández-Armesto's most compelling chapter.
That has crucial consequences for our species.
This leads to a mobility panic at the middle levels which, in turn, has crucial consequences for pinpointing responsibility in the organization.
The formal split of the party into Bolshevism and Menshevism in 1912 had crucial consequences after the outbreak of the Russian Revolution of 1917.
It must then have seemed a terrible chronicle of people forced from their homes – a chronicle that also contained an anxious look at the crucial consequences of a referendum.
This is heralded in a setpiece scene in which one of Henry's throws goes violently awry, with crucial consequences for the other main plotline: the college president Guert Affenlight, a Herman Melville scholar, realises that after a lifetime as a light-hearted heterosexual shagger, he has fallen desperately in love with Henry's teammate Owen.
