Also, DMCA takedown notices properly order certain kinds of intermediaries (not people who have consciously chosen to publish something) to stop facilitating access to allegedly infringing material. They're not properly directed to an alleged copyright infringer himself or herself, and they don't order people to stop downloading things, even if their reason for downloading is apparently to publish the information.
https://en.wikipedia.org/wiki/Online_Copyright_Infringement_...
This is not to say that people don't send "DMCA notices" for anything and everything to anyone and everyone, but those notices are not following the law. (Also, a lawyer can always send a demand letter demanding that someone stop any behavior, but a properly-constructed DMCA notice gives the recipient an extra reason to follow it compared to a run-of-the-mill legal demand—"[a]n OSP who complies with the requirements for a given safe harbor is not liable for money damages", as Wikipedia puts it.)
Yeah, more likely you'd get a Cease-and-Desist. But once the ArchiveTeam publishes it, they'll likely get DMCA'd (though they've survived things like that before).
Not to mention that dying websites or recent acquires are likely to be able to have the legal muster to start threatening archivists.
If you've ever seen a Jason Scott talk, he isn't the sort of guy who gives a shit if you DMCA him while he's sucking up all of your bandwidth archiving your content two days before your servers shut down.