Yeah for sure, you're right in that a machine or even machines across different AZ for HA can have better economics for performance.

But you have api management to sort out and versions to solve which api gateway can do fairly easily.

API gateway is connected to Cloudfront for low latency.

You can simply add a cache for your API.

You have analytics already setup up and ready to go.

Also other things like API keys, auth and cognito integration with other integrations etc that API gateway has.

You can deploy and maintain tens of lambda functions fairly easy, to get something similar you would either have to use some container service like ECS or Kubernetes so have to figure them out compared to just deploying your code with one of the frameworks out there for lambda.