There is a lot of Twitter content out there. Too much for a single instance to proxy. I believe there are projects to mirror specific Twitter accounts to a (personal) Mastodon server so you can switch apps without needing two apps. I'm not sure what the implication would be for privacy/data usage regulations if you open those messages to the public, though; blindly reposting everything may actually violate data privacy laws (yes, even if that information is publicly available).

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).