The share sheet has to be up there as one of the most used parts of the iOS system. As it is the only way for an app to expose all sharing services installed on the device to the user, pretty much every app shows a share sheet controller at some point in its flow. The component supports effectively no customisation points for its appearance or behaviour, so its presentation across every app looks the same. You see it a lot.
I’ve never been particularly thrilled by how the share sheet looks or works. Since iOS 7, the panel is split up into three sections; AirDrop, Share and Action. AirDrop is handy but doesn’t justify a row to itself. Really, AirDrop should be an option in the Share section. Nobody can adequately nail down whether an operation should be catalogued under the Share bucket or the Action bucket. The concepts are too closely intertwined. Sharing is an action and to share is an action. Customers and developers don’t know and don’t care in equal measures. It’s a jumble and people only learn where stuff is by rote, relying on muscle memory rather than any semblance of a sane ordering system.
The share sheet would be greatly improved if it was oriented around people first. Maybe have one section that is about sharing with others (Messages, Mail, Twitter) and then a separate section which is about sharing to yourself (Files, Notes). What if the share sheet showed a list of people rather than a list of apps? The Apple Clips app uses private APIs to do something custom along those lines, substituting the AirDrop row for a list of Messages contact to share your videos with a single tap.
What Gurman describes for iOS 13 sounds somewhat along these lines. It’d be cool if the recommendations would surface sharing shortcuts for people across all apps on the phone, but I wouldn’t be surprised if it was limited to Messages contacts only.