There are stainless chains available for single-speed/internal gear bikes.
Sure, they might not rust, but they need regular lubes anyhow not to wear out too soon.
These can also be fitted with full-cover chaincases. Like your idea, only smaller.
For frequently used external gear bikes, particularly modern ones with 9/10/11 rear sprockets, "pure" mechanical wear will age the parts so fast that keeping them rust-free until elongation forces a replacement isn't much of a challenge. The lube they need for internal friction control will also do well enough to keep the rust away.
Sprocket rust is overwhelmingly a visual and not a functional issue.