People do need to speak in their own person, to learn to be themselves and take positions as their own. A classroom that only corrects grammar and spelling and never asks what is being said will not reach the goals that any education should aim at, that the person himself should be transformed and finish his studies as self-possessed in mind and opinions. The modern emphasis on self-expression and voice notices something real: speech is an act of someone, to someone, about something that matters to them.
It is also true that a student who is afraid to speak needs more than just a scheme of arguments and lessons in how words have meaning. The confidence to stand and speak is also part of the art, not an extra. Sincerity, too, is something students must find, albeit primarily by themselves. A hearer can tell when a speaker is just performing, and that does not build trust in the speaker or his competence on the subject.
The desire to “find a voice to express oneself and worry about language later, if at all” often comes from having been trained in correctness without anyone ever asking the student what he or she thinks and without a place for students to inquire into anything in a genuine way. If that was what school was like for you, then the concern is fair. An education in speech that never reaches something a student cares about like a claim, a story, or a plea has not yet come to teaching what speech truly is or what it is meant to be.
What is true, then, is the need to speak as oneself, and that it is not enough to write correctly in a mindless or disconnected way. But that does not prove that we can somehow express ourselves before words or that we can find our own voice without being taught grammar and logic and rhetoric.