The high level algorithm you describe is basically how async programs work. Glossing over the low level details, you usually implement things in terms of polling. Interrupts and their analogs are far too slow at scale (switching async tasks is in the nanoseconds, these days).

The problem is when there is logic downstream of the task that needs its results and mixed with the results of some synchronous code in between. This is the "function coloring" problem.

Async semantics are designed to insert the logic for handling this (merging of async task results) seamlessly. There are two issues with this, the first is that synchronous code has no way of knowing what to do with asynchronous results (meaningfully), and the second that there has to exist some executor program that handles the merging and scheduling logic.

The thing that makes async "hard" in a language like Rust is that dealing with this problem is extremely difficult when you have no GC, lifetimes, call-by-move, closures that capture by move, and ownership semantics - it makes it verbose to write sound, non-trivial async code. For example, you're forced to introduce the notion of "pinned" data in memory to prevent it from being moved while tasks are switched. Lifetimes become a lot less clear. "Async destructors" don't really exist (what other languages would call finalizers that don't run at the end of lexical scope).

As for the mixing of sync/async code, that's not actually an issue if everything is async. It's trivial to write an executor that makes async calls blocking anyway.