That may be true if you see getting ahead as meaning becoming an ever more senior manager. I do agree that social and verbal skills (and political) skills are important there.

My own verbal and political skills aren't great. I am not a manager! Writing well has been good for me personally in terms of being able to organise my own thoughts better, and to be succinct in a way I can't when I speak.

I find my opinion is consulted frequently partly because I can summarise complex issues and present it in a way others can work with.