Implementing exporting features takes time and money. If such things would come for free, then they would have an obligation.
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 :))