Yes, I believe that audiences should be allowed to interact with a text, but only through the margins, unless it is a defined creative or evolving space like Wikipedia where it is expected that the content may change over time by readers. By allowing comments and interaction with other readers, people can find community, have healthy and friendly debates, and be pushed to think about their views and the views of others. It is a way of extending learning through the discussion of writing and reading.
Granted, not all comments are good comments. Audiences should be limited only in the sense of not being able to troll or spam users (either writers or other people commenting) with unrelated comments or abuse on a text. Plugins like Hypothes.is, it seems, are generally being used by like-minded, curious, and educated people who want to open discussion about different types of thought — the communication appears to be mostly civilized. If authors really were experiencing trolling and spamming through plugins like this, it could be a development of future editions of the plugins to have a scanner that detects fake posts and doesn’t allow them to be posted (again, only with the exception of spam text).
All that being said, I think that writers do not have the right to define who can comment on their text. It may seem at first glance that a simple solution would be to ban all commenting on a text, like Audrey Watter’s post, Un-Annotated. However, by banning all comments and discussion, not only do writers challenge the right to free speech, but drastically cut any chance of their texts building that sense of community, trust, and even following. Posts and articles become “talking at” a person, rather than “talking with” a person. In reading Watter’s post, I immediately felt that she was rude, self-centered, egotistical, and rude, to use polite words. Why would I want to read someone’s article or post when they have such an ego that they don’t think that other people’s comments are valid or important? By making their writing public they are subjecting it to public critique, and people are going to talk about it whether the author likes it or not. If no one is allowed to discuss the piece because the author is too lazy or finds it to difficult to either monitor the comments or relinquish control altogether, they probably shouldn’t be making their writing public.