Fargate does, though. And it's been doing it for at least 5 years, if not more.

Fargate, just like ECS, doesn't natively scale to zero. You can set the minimum number of instances to zero for both, but there is no native mechanism to scale it back to one when traffic arrives. And especially not one that would hold the connection until the container is ready. Not saying it's impossible... Just not native. And it would require extra resources. So the price won't scale to zero without something like Lambda in front of it.