The biggest missed opportunity of ECS that AWS missed was completely hiding the complexity and concerns of managing EC2 instances. If you use ECS you have to deal with the complexity of both and manage those resources. The dream being sold by the container industry is that you don't really care about the machines you're containers are running on. ElasticBeanstalk gets this right because they hide that concern.
ECS is akin to selling git on top of SVN. It doesn't really make sense.
Yeah, that starts taking you down the path to "serverless" - eg. AWS Lambda. I think iron.io has a fully container-based approach here (I've only used their pre-baked containers though).
An application written purely in client-side code, but that still requires a server-side component is not "server-less".
A "server-less" app is one that literally has no need for it. Just because you aren't in control of the server-provided resources the app depends on, doesn't make it "server-less".
ECS is akin to selling git on top of SVN. It doesn't really make sense.
Bryan Cantrill gave a talk about the craziness of running containers on VMs at https://www.youtube.com/watch?v=coFIEH3vXPw.