I'll take "Because Google's entire business model around email is processing it to serve relevant ads next to it, which requires that they be able to read it" for $1000, Alex.
They could still do that in a secure way, client-side, if they wanted: when content is displayed in-browser, javascript could parse it, send home relevant words (on an encrypted channel), and receive relevant ads. The server would have to ensure that data is not saved, or it's anonymously aggregated right away -- you'll have to trust their word on that, but that'll always be the case.
Computationally expensive, maybe, but it's 2013 and browsers can take a bit of abuse. It wouldn't cover people using POP/IMAP, but Joe Average doesn't bother with that geekery anymore. Obviously it would take some time to implement, but it could be done.
They'd also have to do spam filtering client side, parsing the MIME to extract inline images, attachments and so on, sanitize the HTML to protected against XSS attacks, process it for full-text search, filtering into labels, auto-forwarding and really absolutely everything that happens to an email. They all involve "reading" the email.
I'm not saying it'd be a 100% drop-in replacement for what they have now, but it'd be a good approximation, a starting point. I'm a leeching AdBlock user anyway, these days I don't even see what they try to show me...
Why does everyone assumes it's just about the "automated processing" they do?
I'm 100% sure besides showing "relevent ads" in real time as you check your mail, they also keep a huge profile for your account name, cross check with all their other services and mainly search, and generally have a file on you and your preferences.
And that's besides sharing your email with their government friends.
Because this whole kerfluffle is about the fact that by granting Google the ability to spam-filter and process your email, you are giving up your legal expectation of privacy by placing your data into the hands of a third party. It's the lowest common denominator. Sure, they may be doing other stuff, but we know for a fact that they process your email in ways X, Y, and Z, which are what the legal theories are based upon.
Computationally expensive, maybe, but it's 2013 and browsers can take a bit of abuse. It wouldn't cover people using POP/IMAP, but Joe Average doesn't bother with that geekery anymore. Obviously it would take some time to implement, but it could be done.