The first critique group I ever belonged to had an amazing chemistry. There were some traveling members who came and went. There were some unpublished writers who needed some polish on their craft. There was a talented reader. And a couple of English majors, one a working journalist. (Okay the last one was me.)
My current critique group has a different mix of people, and a mix of genres. In my current group, everyone sends a chapter or twenty pages. We read them all every month and discuss. We aim to keep discussions about 30 minutes and fail miserably so we have some late nights.
My old group only one or two people were on the schedule for any given meeting. Those individuals had to email their submission, so those of us who wanted to could read it in advance. Then, the writer had to read the submission out loud. This allowed people who did not have time to read it earlier to hear it.
People protested this policy at first, but I think everyone grew to like it. Not only is it good practice in presence and poise to read your work, but it's a good sign of comfort. If you're uncomfortable reading your work out loud, maybe it's a sign there's something wrong with it.
In addition, listening to the author read the piece allowed all of us to judge how we read. The author's voice could convey sarcasm in a character's dialogue, for example, that we might have perceived as mere stupidity. I remember one of my character's speech patterns coming off very differently when I read them out loud (Étienne's unnatural English became more lyrical, even if 'his' word choice was bad.)
You can fix many problems when you read a work out loud. It becomes obvious where language is clunky. You become more sensitive to the pacing.
Greater Lehigh Valley Writers Group, GLVWG, tries to find venues for authors and writers to share their work. We used to host a special event several times a year with Touchstone Theatre on the southside of Bethlehem. A committee screened the applicants and then members got to read. The attendance was abysmal and I'm told no one applied, yet I know from experience that the committee rejected many applicants. Attendance waned, and location and night of the week contributed.
We have monthly spotlights at our meetings where writers have ten minutes to read. We also participate in festivals.
Some authors read the same chapter every time, whether it be chapter one or one they've rehearsed and honed. They're good chapters, but since the same members of GLVWG tend to make up the audience, I get sick of hearing them. So, when I'm asked to read, I do something different.
And some of my fellow GLVWGers enjoy the concept.
The manuscript of my first book has 400 pages. I let the audience call out numbers, and then I read the page numbers in order. I usually start on the first full paragraph and read until the end of the scene. It has never failed me. It has never landed in a chapter in the French guy's POV and it has never landed in a violent scene or a scene with sexual content. This weirds me out a little.