That tweet is simply dishonest. Expecting Apple to make a migration assistant to help people move off of its platform is absurd and hypocritical.
No, I want to make the migration assistant. How can I access on iOS the same data that Move accesses on Android?
Ask the user for their iCloud credentials. That would get you documents, photos, mail, contacts, calendars, reminders, bookmarks, notes, passwords and many app settings.
Then it should be just a matter of parsing a bunch of plist files and a few SQLite databases.
You can't do it from the device itself, but you can grab all that data over USB if the user has a desktop to sync with...