I would argue that anyone writing anything, at least in any context other than a private journal, can and should care about how their writing comes across to other people. Otherwise what is the point of writing it down and showing it to others rather than just thinking it to oneself or writing it in a private journal?
Sometimes, the purpose is "thinking out loud," seeking feedback on ideas that may not be fully formed, or on a line of thinking that one has not yet fully explored.
There's a saying among writers: there is no writing so bad that it can't be improved, but a blank page is just a blank page.
At the same time, writers are very wary about distributing early drafts too widely. If I know something is bad and am seeking advice on how to fix it, it's not very helpful to tell me that my whole approach is wrong, I'm wasting my time, and I should take up basketweaving instead. Nor am I likely to get useful feedback on a sonnet from someone who thinks poetry is stupid.