Sure. You can re-implement everything starting with the Kernel, as long as you don't have to interface with any of the C microcode on the hardware itself. And, yeah, people are doing this, for instance with Redox OS.
But if you actually want to program something usable in conjunction with existing software, such as Linux, you need to use the C ABI. There is no alternative.
That is nonsense.
As I noted below, low-level OS internals have been reimplemented numerous times, by small teams of volunteers at that.
If you want to "break free", buckle down and do the work.