Yes, my thoughts exactly.

This problem is not solved by monads, but by higher kinded types in general in languages like Haskell. They give you a uniform way to be generic over effects like async (Async<A>) vs sync (Identity<A>). Both of these can be treated as (F<A>) for all A. So a generic Into would look like the following, and no special syntax or semantics would be needed. The type system (if sound) would prevent you from misusing a trait like this.

trait Into<F,T> {
   def into(self): F<T>;
}