In the past 5 years all my projects have been based on AWS Lambda, API Gateway, S3, DynamoDB and other serverless technologies which are only billed for actual usage and network traffic. So they don't cost much unless they actually get heavy load from users.
I love how the justification of numerous AWS services is always "so it can scale" but if and when that scale ever happens, a new architecture is necessary because the costs become untenable.
I haven't seen this happen myself. In projects that I've been involved with, the justification of using serverless services has been to reduce development costs, because you don't have to setup and develop everything from scratch and spend effort maintaining the infrastructure. The ultimate goal is to avoid doing anything else than define the business logic that is unique to the project.
