Just to add my twopenn'orth. I would be more than happy to be cut off as soon as data usage hit the limit. That would certainly signal something desperately wrong going on. As I quite frequently spend a week or two at a time far from phone signals or any reliable internet connection, an early warning system would be difficult.
But then mine is a purely personal account
I also think that maybe the sign up form should have alternative contact details as a requirement. But surely, there is a limit to what you can be expected to do to inform a customer that their account is going haywire