I do think consideration needs to be given to voice. Which is to say I think it's important for a storyteller to give consideration to what he or she sounds like. That's what voice is, really. The sound and style of the individual telling the story.
You're in a room with four friends. They all try to tell you about what happened last night. Each is telling the same story, but each has a different way of expressing what they're saying. One friend might be funny, another might be just-the-facts. A third friend might ruin the whole story, and the fourth friend might provide some sort of somber insight. Everyone has a different voice. You notice this in basic social interactions. You know which "voices" you prefer to hear stories from. The voices you like probably highlight important details and speak with clarity. The voices you don't like probably mumble or forget details or jump around the story in confusing ways that leave you with questions. All of these voices developed naturally, sure. It just happens that you want to listen to some of them and not others.
The same is true of writing. Writers have different voices, and while yes, I agree that those voices develop naturally, I still think they should be considered, nurtured, and often open to change. But all of this is a way of saying that I think your voice is informed not only by your personal taste, but also by the things you learn about the art of the craft. This is storytelling. It's communication. I'm going to hear what you're saying in my head, and what I really want is to fall into your story. To do that, (as a reader) I need you to keep the story moving, describe what's seen, describe what's smelled and felt and heard, and to do all this with enough concrete language that I feel like I'm grounded in something visceral, but never overwhelmed. Your characters have to feel real and alive because I want to care about them. You have to know how long to keep me in a scene, when to heighten the tension, and when to shift the mood without jarring me out of the experience. It's a great and complicated juggling act, to be sure, but I think it's important to note that there's not just one right way to do it. Neither is there one wrong way to do it. What's important is that you have to know what effect your creating inside of me (your reader), and you have to stay ahead of me. You're leading me into your world and telling me your story.
What you have on your side is that the reader wants to enjoy your story and wants to be able to trust you. What you have against you is that the reader has been burned before and is not always so quick to trust. Giving the reader reason to trust you all starts with your voice.