With Fargate-Lambda crossover I wouldn't be running anything 24/7, and it would be a lot less resource intensive than one Lambda-Container per request as well.

Google's App Engine gets / got this right when they first launched, but to make it work they had to demand apps be written for their sandbox (like AWS Lambda), because of which the model isn't as general purpose. Firecracker would allow regular containers to be used this way, making a Firecracker service the first service to allow general purpose servers to be started and stopped (all the way to zero) based on incoming traffic.