The native share dialog is about "I have this piece of content, now share it with one of these other apps", e.g. saving a document locally, or sending it with AirDrop, or saving to Google Drive, or sending as an email attachment, etc.
Installing a site as an app on your homescreen has absolutely nothing to do with sharing content to begin with.
Go back | go forward | share | bookmarks | see all windows
Do you think there should be a separate button just for “Add to Home Screen”?
Or could you just put the standardish share icon on your page and below it say “click here and choose add to Home Screen to…”?
Is that really that much harder than to tell someone to go to the app store?
Most people know how to scroll.
One notably stupid usage of the Share option was (I believe it is no longer how it’s done) adding an image to a hidden folder — that’s something you definitely don’t want to share, yet quite easy to accidentally send to someone during this process.