If it didn't provide value it wouldn't exist.

Maybe it's only legacy, but gmail brings customers to Google and their related services. Escalation then brings them on as paying Customers. As loss leader may make a loss if looked at in a bubble, but if looked at as part of the "Customer Lifecycle" then other areas of profit would likely be much smaller without the free gateway.

It takes me active resistance to avoid Google's paid services, and I'm staunchly independent in relatively rare air. The minor capitulation required to turn into a paying Customer would capture a good percentage of their erstwhile-free gmail users (I would think. Yes, conjecture, interested in explanations of alternative theories).