List it in a database
So I assume that database has to be publicly accessible to be useful, and you have to be able to identify each individual instance in that database.
So what stops someone from saying something outrageous and terrible that gets removed from Twitter, and instead of linking to his tweet people share a link to what he said inside the "removed content database"? Basically they'd be providing hosting for it instead of social media platforms.
I suppose if they make the database searchable, but not linkable - so you can find stuff by manually inputting search terms but it doesn't produce a link that can be used by others - it might work.