I think there is some nuance even for those with institutional access (e.g. field, institution, etc). I am also a researcher (though I hesitate to call myself that), and I read (or skim) through quite a few papers every week, and I very rarely run into a situation where I do not have access through the publisher. It's so uncommon that I very rarely think about (my own) access at all...
I only say this to provide my day-to-day experience, I do think Sci-Hub is a net positive, and I'm certainly in favor of seeing the status quo change.