Playing to the gallery
No doubt this will be hugely popular among editors as a way of sticking it to the man but my initial thoughts are simply "Why?"
The technical arguments are against it - Wikipedia is already an incredibly slow site thanks to the seemingly infinite number of templates and other elements making up each and every page. If a page consists of 100 or more separate elements (fairly common for WP pages) adding even a small overhead to each and every one adds up to a large amount of additional sluggishness. Reducing the cacheability of the site makes matters even worse.
The next consideration is what proportion of activity is actually sensitive. The vast bulk is perfectly innocuous. There may occasionally be things you don't want making public, e.g. looking up those genital warts, but is the average spook or fraudster really looking for things like that? How much traffic is actually and genuinely sensitive in nature? Calling for this kind of thing as a universal default strikes me as a poorly considered knee-jerk reaction that can only harm the project in the long term.