That "supposed to" is an aesthetic/ideological/pragmatic/whatever preference, and one with significant tradeoffs. Again, Scheme's shift/reset gives you the same control over scheduling as Rust's async/await, but you don't need to declare that in the type signature. Rust puts it in the type signature because in the domains Rust targets it is important that you know precisely what kind of code the compiler generates.
> Either way algorithmically the choice has to be explicit, even it it's not a type declaration, it still has to be an explicit declaration somewhere or there is no choice and algorithms have to be expressed in terms of a single concurrency model.
First, we're not talking about two models, but one model with two implementations (imagine that the OS could give you control over scheduling, like here [1]; you'll have the exact same control over the "concurrency model" but without the type declaration -- even in Rust -- although you'll have less precise control over memory footprint). Second, that the language's design dictates that you must tell the compiler in the type signature what it is that your computation does is precisely what creates accidental complexity, as it impacts your code's consumers as well.
In any event, the reason Rust does it is not because of the aesthetic preference you express (that would be true for, say, Haskell) but because the domains it targets require very fine-grained control over resource utilization, which, in turs, require very careful guarantees about the exact code the compiler emits. It's a feature of Rust following C++'s "zero-cost abstractions" philosophy, which is suitable for the domains Rust and C++ target -- not something essential to concurrency. Again, Scheme gives you the same model, and the same control over concurrency, without the type signatures, at the cost of less control over memory footprint, allocation and deallocation.
I think you might be saying that you happen to personally prefer the choices Rust makes (which it makes because of its unique requirements), and that's a perfectly valid preference but it's not universal, let alone essential.
As long as you have shared memory adding type signatures to avoid thinking about and handling concurrent memory access only reduces accidental complexity and limits possibilities to make mistakes.
That is certainly one way to reduce algorithmic mistakes, but it doesn't reduce accidental complexity, and it's not why Rust requires async in the signature. Rust needs to prevent data races even in non-async subroutines that run concurrently. Rust requires async because it implements that feature by compiling an async subroutine rather differently from a non-async one, and the commitment to so-called "zero-cost abstractions" requires the consumers to know how the subroutine is compiled.