First, we need to distinguish between attaching ads to the mail experience versus injecting them into the actual content. In the original post, this service would actually open these letters and insert ads into them. This is not even remotely comparable to what most email providers do. They insert ads around the service, but never actually alter the content of the email. A better analogy would be receiving a discount on branded stamps or allowing advertisements to be displayed on your mailbox.
Second, the use of the term "read" when discussing advertising is asinine, disingenuous and probably detrimental to the conversation (inasmuch as it can provoke unnecessary fear in non-technical users). "Read" implies active evaluation and comprehension, conceivably by a person. The GMail algorithm does not "read" email in the classical sense. It systematically evaluates the content in a way isn't even remotely comparable to "reading." (This doesn't mean that this sort of advertising isn't bad, but portraying it in the way he did is just unnecessary fear mongering.)
Third, the OP seems to decry "keeping a copy" as some sort of violation. GMail is a webmail service. What the fuck are they supposed to do if not store your mail?
Fourth, this service actually seems like a good idea, and is probably something I would use for various types of mail. The price of mail been steadily increasing, and I would be fine with these practices if I knew they were saving me money. I'm willing to tolerate advertising so long as I know that the service is improving my life. Like I do with 95% of the things I use.
In conclusion, this is a very dubious analogy that doesn't really contribute to the pragmatic discussion of cost versus privacy.