I don't think it is unreasonable to assume that the overwhelming majority of people who use computers only use the web browser for 90% of the things they do; the author's viewpoint seems adequate considering that.
I can see how somebody would go down this line of reasoning, but I wouldn't. It requires too many steps when compared with my personal alternative: literally just some paper, an email inbox, and a semi-structured directory of notes available for grepping. I have no brain cells, so anything more than this distracts and overwhelms me to the point of counter productivity.
The browser does have all of our data. It’s our window to brain of humanity. Our neural connection if you will. There is a reason why Google wants to dominate it - you can’t judge quality of search results without knowing how much engagement users have with a site. That data is key and a precious piece of each user many are clamoring for. A tool for thought would only work if the algorithm for it is controllable by the user, not a shadow entity people have no control over. Facebook has been an example of a stuart of our browser - deciding what is suggested, puppeteering all content. You can package your data and plug GPT 4 into it on each future keystroke, but an important question to answer is why? Will this tool be an agent of the user or a wind blowing them in whatever direction the writers decide.
https://www.jsoftware.com/papers/tot1.htm