The user probably wants to know where they are in a list while scrolling, but otherwise it shouldn't be a problem to reclaim that screen space by hiding the scroll bar when they're done.
That reflects how things work on macOS and iOS right now, the scroll bar disappears when you stop scrolling. However, that does not apply to "pop-in" elements like the share pane. It operates like a slidable component on-top of the current app, it does not even have a scroll bar in theory, because from its point of view there is nothing to scroll. Whether that's a good choice to begin with is open to debate, but I assume Apple's design team would be averse to showing a positioning indicator due to the fact that it would break their skeuomorphism.