I spun up my own Archivebox after archive.org wouldn't let me archive some news stories and I heard about them removing other content. Instead of calling the Internet Archive the wayback machine, I now call it the maybe back machine. IA is a centralized service and subject to the government and other powerful pressures any centralized popular service faces. If you want to archive something that might now or in future want to be erased by people in power, you should decentralize it to somewhere like an archivebox. This is especially useful if you are writing a book with many citations.
As the ArchiveBox creator I give a good chunk of the ArchiveBox donations I get to Archive.org, and I talk with them a few times a year to share knowledge. I think both centralized and decentralized approaches have their place, neither one can cover every use-case or doomsday scenario fully.
ArchiveBox also saves URLs it ingests to Archive.org by default for this reason!
Are you assuming "people in power" were tied to those situations, though? Specifically, did you check if they were following a robots.txt? I have some criticisms for how they handle robots.txt, but if that's the root cause then it paints a very different picture.
I recall trying to archive a story on a Des Moines local news site. It was publicly available and searchable. I understand people can request of IA not to allow their content to be stored, and there are situations where content is removed on request. Beyond that, it is all opaque to me what goes on there.
