On the larger issues, & specific to the Internet Archive:

You should assume there are several other larger "dark" web archives, by nations and large private organizations, collected without the awareness or available-remedies of the Internet Archive's or various national library public efforts. There are also uncountable other private and ad-hoc collections. Depending on what kinds of harms you expect from retained copies of older writings, these may be far larger threats than any holdings of an open, public, correctable non-profit library.

I would emphasize that anyone (like a web host or app) who gave any authors, especially the young & net-novices, the impression that something would stay private, or recallable, after being placed on a public webserver, at a published link, and open to browsing by all, did those authors a disservice by mis-informing them of risks, and the best-practices for preserving privacy.

That the Archive's well-identified, blockable crawlers sometimes surprise people with what they collect, and then make-available for lookup, helps correct that misunderstanding, both for individuals and the wider culture. Any "chilling effect" is unfortunate, but it's inherent to the web technology & practices of many independent actors. It's moreso documented, than created, by the Archive's own activities. And further – at least with respect to the Wayback Machine – the surprise availability is then fairly straightforward to undo, and prevent from recurring.

The broader risk that anything on the web – once offered to the public – will remain available from others persists no matter what the Archive does. Those concerned about such risks should take extra privacy-preserving steps, because blocking the Archive's crawls, or correcting the Wayback Machine, only limits this one polite, above-ground actor.

Those are exactly what hundreds-of-years of copyright law, by explicit statute and court interpretation, have addressed. The precedents for private actors, and especially noncommercial entities like libraries & schools, to retain those copies, and to a large extent, reshare/redisplay them, are very strong.

Further, by design, every delivery of content across the web necessarily creates copies at every network node, and perhaps multiple proxies/caches, on the way to the web browser. The web browser necessarily creates & displays a copy – and normally keeps one, at least for a little while for user convenience. Anyone choosing to core web protocols has already implicitly authorized lots of necessary copying.

Why wouldn't the recipients of such display-copies, and especially non-profit libraries, have on the web the same assumed right to keep/transfer/format-shift/redisplay that freely-delivered copy, in the same way they've always had the right to do with copyrighted books/magazines/newspapers/newsletters/pamphlets/flyers?

If copyright maximalists & DRM fans want a new right to remotely recall/destroy such copies – indefinitely, retroactively, and unlike the traditional copyright balancing-of-interests – they should make the case to lawmakers & courts for that, or use the technical measures already built-into the web for expressing such limits, and opting-out of the web's and copyright's defaults. You shouldn't let them simply assert that right without reasoning or a case for why it's better than tradition. Nor, allege criminality or 'bad-faith' against people just using the worldwide-web as it was designed, and enjoying readers' rights as they've been traditionally interpreted.