An interesting conversation. I'd never come across the term 'beta' til I came here. Perhaps it is a fanfic thing. For me 'beta' always meant a release eg of software, that was not final - it was past the design stage but needed to be tested further, usually in a live situation, to find and fix the final bugs.
Here I assume the word is used instead of editor. Editors are, apparently the bane of writers. Always changing their work. Except there are different types of editing - for grammar, punctuation, sentence, paragraph construction as well as continuity. It is not an editors job to change the story because the story is the author's job.
So at the very least all of us could do with a beta to fix our spelling errors and basic grammar and construction. But a beta could also perform the task of pointing to a more structured, cohesive plot, pick up charachter portrayals/developments that are incongruous with preceding parts of the stories and or canon charachter traits, time lapses that aren't explained, suggest the correct genre, etc. I'm sure we've all read a story or a meta, loved the basic plot, or idea but the grammar and or spelling mistakes drives us batty and sometimes drive us away.
I think I would be a dreadful beta. I'd be wanting to rewrite the story, I'm sure. Having said that I'm also aware that a beta would save me the countless edits I make to something I've posted just for grammar and sentence construction. A beta could also suggest a different way to say something that would give the story, or at least, that part of it, more impact. Even a very good writer needs the services of a good beta/editor.
A good working relationship between a beta and a writer, or in RL an editor and a writer, should produce a story fiction or non fiction that will have the readers come back for more.