The finances work out in a couple ways. First, developers are expensive so productivity improvements on the cloud saves money and speeds delivery. Managed services (storage, queue, email, database) can have great productivity gains. This is also faster delivery or smaller team sizes. Why hire a sysadmin, db admin, etc when AWS has managed services that remove (or reduce) the need for those roles. Keep your headcount low and move fast.

The math is different for different companies, workloads, etc.