Unfortunately IA lost all credibility in my eyes, when they decided that one journalist in particular gets to decide that none of their (awful) tweets should be archived[1].
I understand not allowing certain things to be archived, but the tweets of a public person, especially one who works as a news-maker, should certainly be in the allowed list.
E: And just to be clear, this was before said writer set their tweets to private.
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[1] https://web.archive.org/web/20230000000000*/https://twitter....