am I giving the work to the core in the wrong way?
Yes, you are giving one request to Tokio and requiring that it complete before starting the next request. You've taken asynchronous code and forced it to be sequential.
You need to give the reactor a single future that will perform different kinds of concurrent work.
Hyper 0.14
use futures::prelude::*;
use hyper::{body, client::Client};
use std::{
    io::{self, Write},
    iter,
};
use tokio;
const N_CONCURRENT: usize = 1;
#[tokio::main]
async fn main() {
    let client = Client::new();
    let uri = "http://httpbin.org/ip".parse().unwrap();
    let uris = iter::repeat(uri).take(50);
    stream::iter(uris)
        .map(move |uri| client.get(uri))
        .buffer_unordered(N_CONCURRENT)
        .then(|res| async {
            let res = res.expect("Error making request: {}");
            println!("Response: {}", res.status());
            body::to_bytes(res).await.expect("Error reading body")
        })
        .for_each(|body| async move {
            io::stdout().write_all(&body).expect("Error writing body");
        })
        .await;
}
With N_CONCURRENT set to 1:
real    1.119   1119085us
user    0.012   12021us
sys     0.011   11459us
And set to 10:
real    0.216   216285us
user    0.014   13596us
sys     0.021   20640us
Cargo.toml
[dependencies]
futures = "0.3.17"
hyper = { version = "0.14.13", features = ["client", "http1", "tcp"] }
tokio = { version = "1.12.0", features = ["full"] }
Hyper 0.12
use futures::{stream, Future, Stream}; // 0.1.25
use hyper::Client; // 0.12.23
use std::{
    io::{self, Write},
    iter,
};
use tokio; // 0.1.15
const N_CONCURRENT: usize = 1;
fn main() {
    let client = Client::new();
    let uri = "http://httpbin.org/ip".parse().unwrap();
    let uris = iter::repeat(uri).take(50);
    let work = stream::iter_ok(uris)
        .map(move |uri| client.get(uri))
        .buffer_unordered(N_CONCURRENT)
        .and_then(|res| {
            println!("Response: {}", res.status());
            res.into_body()
                .concat2()
                .map_err(|e| panic!("Error collecting body: {}", e))
        })
        .for_each(|body| {
            io::stdout()
                .write_all(&body)
                .map_err(|e| panic!("Error writing: {}", e))
        })
        .map_err(|e| panic!("Error making request: {}", e));
    tokio::run(work);
}
With N_CONCURRENT set to 1:
real    0m2.279s
user    0m0.193s
sys     0m0.065s
And set to 10:
real    0m0.529s
user    0m0.186s
sys     0m0.075s
See also: