>"checking the requirements for various items (passport application, driving license application, various benefits and tax breaks) would benefit more from a simple page, and a local cache than they would from encryption..."
So I know you're going on holiday soon so I can plan who and when to burgle. I know you'll be getting a new car in the not-so-distant future, so I can advertise accordingly. And I know what tax breaks you're looking into, so I know how many dependents you have and also have a reasonable handle on how much you earn.
In addition, I can splice your internet connection, adjust the content being delivered to you and give you advice that strongly encourages the use of my (paid-for) services.
There's almost no downside (HTTPS is easy as pie to set up these days and computers have long-since gotten past the point where you'll notice a performance hit). I don't see what your argument here is based on.