

If your goal is small binaries, it’s possible to get them with Rust, too: https://github.com/johnthagen/min-sized-rust
There are a variety of reasons why Rust binaries tend to be bigger unless you follow some of those guidelines, but the biggest one (and actually not something those guidelines recommend changing!) is that C is generally dynamically linked against a system version of the C standard library, whereas Rust binaries are statically linked by default, meaning that the binary is actually self-contained.
I think you’re making some poorly-researched assumptions.
In the embedded world, there often aren’t “system libraries,” depending on just what you’re targeting. But if, for some reason, you really do want to use libc but not the Rust standard library, you can certainly do that; for instance, here’s a crate that reimplements the Rust standard library’s output and formatting capabilities using libc: https://github.com/mmastrac/rust-libc-print
Rust provides essentially the same memory control as C does. You can also have inline assembly in Rust, just as in C.