Not entirely true. The largest use case we see for Lambda is as the compute service for an API backend provisioned with API Gateway (so a full application backend) with synchronous responses over HTTP (so rapid response provided within milliseconds) and for mundane tasks that store data in a database just like a regular web application.
The perfect use case we see repeatedly is for high volume HTTP requests to API Gateway endpoints that trigger Lambda functions that respond in less than a second depending on what compute is running.
Reads as the thing AWS wants people to use Lambda for.
Running Lambda as a back-end is one of the most expensive options (especially when high load comes in, as a parent pointed out). So no question, that's what they want to sell.
The perfect use case we see repeatedly is for high volume HTTP requests to API Gateway endpoints that trigger Lambda functions that respond in less than a second depending on what compute is running.