There are solid reasons to put your browser executable and storage other than on your principle desktop in the first place.
That still leaves the attack-surface of browser-based activities (do you really want your recreational activities sites interacting with your financial services?), but both gives the option for fresh respawns (OS and/or browser) and physical and network isolation of your local storage and data from your browser.
(This presumes hygiene on any browser-based downloads as well, of course.)
In general, the idea that we'd want all our data on a globally-accessible network is seeming increasingly unwise to me over time, given both technical and political developments.
Late edit: Oh, and Browsh: text-only browser-via-proxy supporting CSS/JS.