The better analogy is letting the USPS read our postcards and use information from that to create better advertisements to help pay for the service. You have a legitimate right to privacy with a sealed envelope (according to the law) and you have that same right to privacy if you seal your packets (i.e. encrypt them). In fact, your ability to protect your private packets is much stronger than your ability to protect your private mail.
Now, my personal opinion on the matter is that a decent company shouldn't use DPI in such ways, but it is my responsibility to protect information I want to keep private and to educate others to do the same.