Rust absolutely benefits embedded software. A big reason is that the type system allows libraries to let you enforce invariants at compile time.
For example, your i2c controller only supports two specific pins and they have to be in a specific mode? That can be a compile error if you make a mistake.
> just hide the register bits in a private TU and expose i2c_init(), i2c_write(), etc.
That's not a zero cost abstraction, unless these "functions" are actually provided in an include file. Embedded programming is often performance sensitive, so this can matter.
It’s a chore because the alternative in C is to do things perfectly without the machine doubling checking your work. That assumption does not hold with tools other than C.
For example, your i2c controller only supports two specific pins and they have to be in a specific mode? That can be a compile error if you make a mistake.