It boggles my mind that anyone would seriously need to ask that question.
Entitlement much?
Yes, it would not be nice of them to do it. Yes, it could be bad for their image and ultimately even their business to do it. No, they shouldn't do it.
If it's just shutting down an account, probably true. But if GMail started giving people's email accounts to other people, which would allow other people to start receiving their bank statements, business correspondence, password resets, etc., I don't think it would be an open/shut case. Courts would likely want to do something about it, and there are various legal theories that are broad enough to potentially be employed, e.g. detrimental reliance on representations, tortious interference, or contributory negligence.
Consider an extreme case: someone is using GMail for their business. Google cuts a deal with their competitor to intercept the business's email and send it to the competitor. Would this be legal? If Gmail accounts and the email in them are unrestricted Google property that it may dispose of as it wishes, then it would be; Google can of course sell its own internal email to anybody it wants. But my guess is that this scenario wouldn't be legal, despite the fact that the business is not paying Google for the email account, and Google owns the servers that are receiving the mail.
It has nothing to do with entitlement, I am pretty sure a lot of people would be surprised to know that their gmail account could be given to someone else at random.
A lot of people are surprised about a lot of things - most people don't know what's in their food, just off the top of my head - but that doesn't mean they have some right to have things they way they thought they were. There's just so far a sense of outrage will take you.
IANAL, but I could see a case being made against giving your email address to someone else - seeing as it would result in that someone else receiving your previously private email in the future (e.g. they could easily compromise any accounts registered through the gmail address).
