I think there was little traction in curl, because Rust users can just use hyper directly.

https://lib.rs/curl is used in 1000 packages, https://lib.rs/hyper is in 21,000 packages.

Curl is big and supports lots of protocols, but Rust doesn't need a one-stop-shop for all of them. HTTPS covers majority of uses, and Rust has separate packages for mail, ftp, websockets, etc.