What you're talking about is very sensible and I was equally surprised that Airflow didn't support long running tasks but you can layer over the workflow orchestration system a kind of ad-hoc higher order system that enables what you speak of. It kind of feels ugly but can get a lot done.
There are definitely ways to accomplish what you are saying using a combination of DockerOperators + ephemeral WebSocket servers running within containers as semi-long running tasks, and basically just have a dumb/heavy Redis container that persists to run streaming between the coordination architecture across these data flow jobs.
"Work in progress" lol!
EDIT: updating Airflow from 1.10.10 to 2.1.2 recently was a huge pain in the ass for what it's worth, good luck to all our fellow protagonists that are dealing with multi tens of thousands of task DAG setups... big ooooff