I posed this question to JR Raphael of Android Intelligence, and he said the main problem is that there are two kinds of share sheets -- a system share sheet and app-specific custom share sheets. The ability to pin your favorites is in the system share sheet, but not available in custom share sheets, and it can be pretty inconsistent when either of those show up, depending on the app. You'd think that Google's own apps would always use the system share sheet, but nope, that's not the case.
Sigh. All we can do at this point is keep sending feedback to Google.:-\