This made me smile because I too have been puzzled by the hype around serverless. I'm sure it does have its uses but it wouldn't provide an acceptable solution for any of the problems we currently need to solve. Not saying that won't change but I do find it vaguely irritating that serverless has at times been presented to me as an end to all woes when that clearly is not the case.
Having just spent sometime actually learning "serverless" between lambda and GCP I am presently baffled as to how this isn't weirdly hard to use docker containers.
To your point, it seems like AWS ECS really is the best of both. You get the no-infrastructure benefits of Lambda with the flexibility/control of a docker container.
You keep the ability to exercise a fair amount of control, easily, and clearly.
And you don't sit inside really opaque execution environment.
Sure, the scaling and provisioning of those Docker containers is opaque, but I'm much more willing to deal with it at that level.
I'm guessing you're thinking of their Fargate option. ECS itself is not terribly opaque (at least to my eyes). Fargate's biggest downside is its own cold start times - unlike Lambda, there's no caching to give you warm starts on jobs.
The flip side - so long as its a service and not a job, who cares? :D