There is Redox, for the full-on ambitious plan to write an OS from scratch: https://www.redox-os.org
Then there's the Rust rewrite of coreutils: https://github.com/uutils/coreutils
Someone also did the research on building a Linux kernel module in Rust, though it seems like quite the hassle: https://github.com/tsgates/rust.ko
There's also a project to essentially wrap seL4 in Rust to build apps on top of it:
There's also intermezzOS, which is a (still being written) "build-your-own-OS" tutorial project that uses Rust.
It's also worth noting that Rust isn't magic and especially when doing very low-level stuff the use of unsafe blocks is unavoidable. On the other hand, by isolating unsafe behavior you know where it is and can test it very carefully and keep it as contained as possible.
Are there any situations where unsafe code cannot be avoided at all, where there exists a program-theory proof that unsafe code must be used?
If it's for performance reasons, then a new safe language construct could be introduced to replace it - such as how a safe range-based loop eliminates the need for bounds-checking with fixed-length arrays.
The project is called Quantum: https://wiki.mozilla.org/Quantum
I'm pretty impressed by the progress the project has already made.
If I had a bit more time I'd love to contribute!
While HTML/CSS/JavaScript have historic oddities these only go back 15-20 years. x86/IBMPC legacy has 40years of horrible decisions burned into it.
To that end there is a lot of progress in the systems world, but core infrastructure isn't something you just rewrite/replace overnight.
* Redox is a full micro-kernel OS from scratch [1]
* Rustls is a TLSv1.3 compliant server [2]
* Ring is _mostly_ Rust (uses some C for where Rust doesn't work) [3]
* Subtle is consistent time library for building crypto libraries with [4]
* An entire webbrowser (well the JS is still C++) [5]
* A terminal emulator [6]
* A grep replacement [7]
* A non feature complete tar archiver that supports gzip, bzip2, xz, zstd, brotli, and lz4 [8]
The real challenge is Rust has been _released_ for 2 years now. C is approaching 50 years old. C/C++ has _a lot_ of momentum, history, and existent libraries.
[1] https://github.com/redox-os/redox
[2] https://github.com/ctz/rustls
[3] https://github.com/briansmith/ring
[4] https://github.com/isislovecruft/subtle
[5] https://github.com/servo/servo
[6] https://github.com/jwilm/alacritty