I'm fully on board with this. I've been trying to get people to realize the power of the browser as a ubiquitous runtime for local software (akin to the way that /usr/bin/python and /bin/bash are situated to run scripts loaded from disk). But there's evidence of an obvious mental block when I try engaging with people. It's as if when you speak about the browser, people immediately start slipping and don't stop until…
I got here because I'm interested in "Narrative Trails", a concept that was proposed by Bush in "As We May Think" in 1945. The idea of weaving together a set of documents to convey a complex context is quite intriguing to me. It started as a purity thing for me (the underlying documents should be read-only, markup should be separate), and morphed into this view far more sympathetic to collage.
As for saving things locally, I think I'm going to proxy the web locally and save everything in a 2 terabyte ring buffer. Anything that gets referenced with a link gets moved to permanent storage. That way I'll never have to deal with a broken link again.