The problem is that your split-up async function ceases to be a normal function. It doesn't use the stack in a similar way than normal functions. Furthermore, the executor / event loop is required for running those async functions.
So you can't call async functions from normal functions, because they aren't. You need to create an event loop and then hand the task over for it to process it. Your world splits up into sync and async functions.
Go and Erlang are going with the similar "lightweight thread" approach as Java's project Loom. On the other hand, JS, Python and C# have gone with async. I'm not sure if these languages actually need async, going with something similar as project Loom would have also fit, and would have been simpler from the user perspective, perhaps? But hindsight is 20/20.
Rust has also gone async, and I'd argue it's the only one of the pack who really have async/await as a necessity - this is because of two design requirements that differ from Java, C#, Python and JS: 1) must have native-level performance when calling foreign code that expects a C-like stack. Something like Loom doesn't provide that. 2) must not have an implicit default runtime.