Personally, I would rather have a print.css that hides everything but a message that says "save the trees, don't print an article only to discard it after".
We do have some clients that ask for their website to be printable, but it's mostly clients that are in the legal or medical business. It doesn't come in regular contracts, the client has to ask for it.
http://www.dailymail.co.uk/news/article-2290444/Madness-How-...
http://www.theguardian.com/business/2012/feb/21/drax-scraps-...
More than anything else, I just wanted to bring attention to something I think many people don’t know about, because I think it’s mostly a case of people not minding printed web pages rather than them not caring.
https://news.ycombinator.com/item?id=7609711
I would find this message rather rude. I am interested in saving trees, but do not think technology offers me a solution yet. I print out of necessity.
I'm talking people going to a news website, printing the article, reading it and discarding the resulting paper afterward. Unless you need to annotate or use the printed articles in some of the ways you listed, you shouldn't be printing all the articles you see.
It still makes me suffer a lot though because optimizing for printing us clearly not the norm.
Also, I frequently cache articles by printing to PDFs not knowing a better way of capturing a static snapshot of a web page into a single file. I do not print these, but the resulting PDFs suffer from the same layout issues. Also, links do not get converted. (Several PDF software makers supply plugins for Microsoft Office, but almost none for web browsers.) I am happy to hear if someone has a better solution for this (other than using Internet archiving for such cashing).