Students have their own gmail accounts vs having accounts issued by the school, who is then responsible for them in some capacity. There is also a cost per-account in Google Apps for Education.
But a system where students brought their own outside accounts would have all sorts of other complexities; in fact, I think they would add up to a greater overall workload. Similarly, the alternative would come with its own set of costs, and the fact that schools are expected to sign up for this service, and that they're generally not run by stupid people, would suggest to me that the overall total cost of ownership, including the fees Google charges, would be less than doing it the other way.
