I think if the site is publicly accessible, it's basic Internet civility to allow IA to archive it, but especially so for a newspaper. It's a question of respect for your users and for journalism.

If they have fears about losing revenue - and although I find them silly - there are other ways of going about it, such as only allowing access to pages some weeks or months after they've been published.

Okay, I completely agree about newspapers, maybe other things as well. But you said people who ban IA from their site could be criticized, there are plenty of other comments along those lines, and I just don't see it. As advice, sure: if you post it on the internet, assume it will stick around forever, because that could happen. But still, there are personal public websites, if you know what I mean. They're not secret, they're not hidden, they are accessible to the public -- but they do not belong to the public, they are not like a public park or road. And sometimes, a website is more thinking aloud, or talking to oneself, than writing a book that then belongs to your "audience".

Civility is a good keyword, and while this may be a bit of a stretch, imagine sitting in public cafés and writing down what people say, and then criticizing people for lowering their voice and turning their back so you can't read their lips, even though you genuinely mean well, and just want to preserve daily public life for future historians. In general, this is what this attitude of "the internet" feeling entitled to whatever was ever posted anywhere feels to me. Maybe I just don't get it, but I really don't get it.

I think the question wether a private conversation should be recorded just because it's in public, just because you can, is kind of a no-brainer, but here are ones I don't have an answer to: Should an artist be allowed to make a performance and ask it to not be recorded? Should someone be able to hold a political speech and ask the same? For me the answers are kind yes, and no-ish... but what about political art? Are we allowed to try to influence people, and then try to erase the traces? Now that is tricky, and I may have ended up ranting myself into agreeing more with the IA "side" of the argument than I expected to. Because either something is personal, trivial in one way or another, or commercial and/or political. Personal things I think should be respected, but commercial and political things shouldn't be, they do belong to historians. Well, fuck.

[this is why I "blog" bit, actually -- because posting stuff online makes me think harder about them than I would otherwise, I don't even need an actual audience for that, just the possibility of one -- but that's also why I don't feel great about all of that floating around forever, it's all rather temporary in nature, a process.. and the person who wrote stuff a year ago does not exist anymore, so why should the name of this current person be attached to it?]

I think conflating a publicly accessible website with a private conversation - even if in a public setting - is specious. That said, I concede the point that some websites are meant to belong to the deep web, and while I wouldn't feel guilty about archiving it for personal use anyway, I wouldn't blame the author for banning archivers.

I'd say my general rule is closer to: if you allow search engines, you should allow IA.

W.r.t. your last question, historically the solution to that problem was simple and elegant: people used pen names to write what they didn't want to bind permanently to them. This way is also safer from unauthorized archiving - not everyone is as respectful of the author's wishes as IA.