This is a great rundown of the issues at play with this! I've recently been thinking about it too. The vagueness/multifacetedness of the beta role is why I think it's important to discuss with a beta what, exactly, you want them to do. I've worked with betas where we actually did developmental editing, and it really helped me improve on a deeper level than just making my prose better. (One of the most important questions a beta ever asked me was "What do you want a reader to take away from this fic?") But not everyone knows how to work on a story on all possible levels, from big-picture conceptual stuff, to structure, to individual word choices.

Writing isn't just one skill, but rather a suite of interconnected skills, and the same goes for critical reading.