Yes of course you could do this in Rust. It's just that every resource out there promotes the usage of Cargo, and sells this as an "improvement" over the old school way of managing dependencies manually.
it's mainly an improvement because the rust ecosystem has a standardized way to build and distribute packages, so you can reliably add a dependency without build system pain. If you don't think having a reference to a central repo is a good way to go, you can vendor or even just pin your dependencies.
Cargo will let you vendor code into your repo easily.
I think you’re conflating the tool, with how people manage deps.
https://doc.rust-lang.org/cargo/commands/cargo-vendor.html