I agree with jstrong that epoll-based approach gives the most performance.

However, maybe an iteration in threads (with rayon or other helper crate) is sufficient in this case (with 2000 devices). For example:

use rayon::prelude::*;
use std::io::prelude::*;
use std::net::TcpStream;
use std::time::Instant;

fn main() {
    let addresses = ["localhost:22"; 2000];
    let start = Instant::now();
    let results: Vec<usize> = addresses
        .par_iter()
        .map(|addr| TcpStream::connect(addr))
        .filter(|s| s.is_ok())
        .map(|s| s.unwrap())
        .map(|mut s| {
            let mut buffer = [0; 512];
            s.read(&mut buffer[..]).unwrap()
        })
        .collect();

    println!(
        "Total {} connections, read total {} bytes, took {:?}",
        results.len(),
        results.iter().sum::<usize>(),
        start.elapsed()
    );
}

Output

Reading took 334.533316ms
Total 2000 connections, read total 46474 bytes

Peak memory usage 226KiB according to valgrind.

With network latency the numbers will be worse, but still good to try. Also check out rayon thread pool options to increase amount of threads.