Yes it does. The internet forgets lots of things. And anyway, this isn't about completely removing information from the internet, but removing it from the "front" of the internet, aka. news sites that show up at the top of google searches and are more trustworthy than some discussion from 9 years ago on a now half-dead message board.

It does, moreso than ever before, because fast internet speeds allow on-demand access and no-one has to download anything. Media files like Youtube videos or podcast episodes rarely get archived, at least in a publicly accessible way. Once they are taken down, they are usually gone.

There's a particular 1970s Pan Am ad I regret not saving: just a man looking at the camera and challenging the viewer to "do the things you always wanted to do" instead of worrying too much. Few years ago it got taken down from Youtube and I haven't been able to find it anywhere else online.