I imagine they could completely shut down all unpaid gmail access at any moment with no legal implications (though I haven't read the fine print, and in that extreme case the courts would probably step in just to keep the country running smoothly).
What precedent is there to support your hypothetical lawsuit? I kind of disagree, they would just get a lot of negative PR.
Yes, it's your stuff and I don't agree with the parent. But you're not necessarily entitled to features for an easy export of that stuff. That's the kind of agreement that has to be explicit in order for you to feel entitled.
Anyway, if you want fair treatment and to feel like a customer and not a product, you should pay for using it. I'm on Google Apps, I have my own domain and email address, I can always move, I don't get adds, I can use the Exchange protocol, I have more options for importing/exporting and the email support has been very responsive for me. From what I hear Office 365 is a solid option lately and there's also FastMail.fm and others.
And btw, allowing them to advertise in your Inbox does not make you the customer, you're just a user of free stuff. And free stuff is great, but not when you depend on it (unless it's open-source :))
So in other words, it really is your stuff. Imagine if they locked your accounts from you out of malice - it's legal gray area, since I don't believe there have been any court cases, but I'm pretty sure the result would be obvious. You would easily be able to sue them to get back your access to it.