Engagement with the audience also is a significant factor for making social media enjoyable. A read-only mirror of Twitter would be very boring, because you can respond/tag/whatever you want for all eternity, but the Twitter authors would never notice.
Such a system would work for people primarily using Mastodon that cross-post to Twitter; you could add Twitter replies to the Mastodon replies and get a mixed content stream (that Twitter users might miss half of when discussions respond to as-of-yet unproxied messages).
Nitter exists and it is open source. Why not add a mastodon API to it?
The existence of such a thing in no way has anything to do with existing mastodon instances TOS / acceptable use relationship with twitter (if such a relationship even exists).0
Source code: https://github.com/NicolasConstant/BirdsiteLive Official instance: https://beta.birdsite.live/
In the example of Twitter, Nitter already exists as an alternative front-end. Now what if there's a Mastodon instance that uses Nitter to wrap official Twitter content and serve it as if it where the twitter.com mastodon instance? Again it would need to be a read-only version as Twitter is not Mastodon but it would help fill the content gap for sure.
Now Mastodon might not have a content issue but PeerTube for example very well has and in that case masquerading YouTube as a PeerTube instance would become very interesting.