But considering what Wikipedia is, users wanting increased privacy could just download a copy of the encyclopedia and do their searches offline. Wikimedia makes data dumps of their user-generated content (UGC) available to the public. (Don't you wish all mega-websites relying on UGC did that?)
There was a time before the internet when we used volumes of paper bound encyclopedias. These were not written by laypeople and they were not free. Few people owned their own set of volumes of Brittanica's encyclopedia. They used someone else's copy, e.g., a library's.
But imagine if Brittanica offered _free_ copies of their encyclopedia that could somehow fit in your pocket (as is possible now through digitization and Wikipedia).
Would you continue to use a copy belonging to someone else everytime you had to look something up? Why wouldn't you obtain a copy for yourself?
What if... Wikipedia's data dumps were small enough. Wikipedia content was, overall, static enough. Storage was cheap enough. Download speeds were fast enough. And you could get your very own copy of the encyclopedia.
Compared to the speed, reliability and privacy of offline reading, grabbing specific articles piecemeal via HTTPS simply cannot compare.
See OpenMoko's WikiReader as an example implementation. It's on Github.