I cannot speak for the user you replied to, but to answer this question:
> Do you only have a single thread of tasks you're doing at any given time on your machine, all of whose resources are torn down and rebuilt from scratch when needed?
Yes, absolutely, at least when it comes to my web browser.
I run Firefox Nightly and intentionally use its prompt to restart for an update as a prompt to consider whether I should close the things I have open. I'll sometimes ignore the update for a few hours, but not usually longer than that.
If I need to retain some information over a period of more than a few hours, I'll transfer it to a note-taking app or something similar. Habitually not keeping a large number of tabs open helps me maintain focus to some extent, and deliberating over whether to close a tab or window presents and opportunity to think about extracting a snippet for storage elsewhere.
To me the idea of keeping an entire webpage open as a method of storing what is likely a very small subset of what it contains just doesn't seem "right", regardless of actual resource consumption on the computer I'm using.