Why don't the async methods' return types implement Sync in addition to Send?

I'm using the async_trait crate to define an async method on a trait. I intend to transform the Future it returns into a Stream, wrap the Stream in an Arc and send the Arc over to multiple threads. Minimal reproducible code is as follows:

use async_trait::async_trait;
use futures::stream::{unfold, Stream};
use std::sync::Arc;
use tokio::runtime::Runtime;

#[async_trait]
trait Trait: Send + Sync {
    async fn do_something(&self) -> i32;
}

async fn use_trait<T: Trait>(x: &T) {
    let boxed: Arc<Box<dyn Stream<Item = i32> + Send + Sync>>;
    let lazy_poller = unfold(None, move |state| async move {
        if let Some(value) = state {
            Some((value, Some(value)))
        } else {
            let value = x.do_something().await;
            Some((value, Some(value)))
        }
    });
    boxed = Arc::new(Box::new(lazy_poller));
    let boxed_clone = boxed.clone();
    let rt = Runtime::new().unwrap();
    rt.block_on(async {
        let _moved = boxed_clone;
        // Do something with `_moved.next()`
    });
}

However it compiled with the following error:

error: future cannot be shared between threads safely
  --> src/main.rs:21:22
   |
21 |     boxed = Arc::new(Box::new(lazy_poller));
   |                      ^^^^^^^^^^^^^^^^^^^^^ future created by async block is not `Sync`
   |
   = help: the trait `Sync` is not implemented for `dyn futures::Future<Output = i32> + std::marker::Send`
note: future is not `Sync` as it awaits another future which is not `Sync`
  --> src/main.rs:17:25
   |
17 |             let value = x.do_something().await;
   |                         ^^^^^^^^^^^^^^^^ await occurs here on type `Pin<Box<dyn futures::Future<Output = i32> + std::marker::Send>>`, which is not `Sync`
   = note: required for the cast to the object type `dyn Stream<Item = i32> + Sync + std::marker::Send`

It seems that async_trait desugars the async methods' return types as Pin<Box<dyn Future<...> + Send>>, without specifying Sync. However I thought it would also be fairly common to require Futures to be Sync, in addition to Send.

My questions are:

How should I specify the async method's return type to be Sync, and
Why does async_trait not specify Sync for the return types automatically?

dtolnay / async-trait

Why don't the async methods' return types implement Sync in addition to Send? #142