That's just not true. From Firefox and Chromium browsers, I can share an image, and when I send it to someone over Signal or Discord, they get the image, not the link. Voyager and Jerboa for Lemmy both share the image directly, no link. Tusky for Mastodon can share images directly. The NextCloud app for Android lets me share an image from my cloud storage, not a link to it. The picture gallery on my phone can send images directly without hosting and then linking.
And all these use a nearly if not entirely identical UI for it, which heavily implies to me that there is some underlying feature of Android that all of these apps are using to offload the work of reimplementation.