In general, the debugger is not intentionally made unavailable but rather the "properietary" one is just the original Visual Studio debugger extracted into a standalone package adapted to cross-platform.
Other than that, CoreCLR exposes rich debugger API, and debugger implementations just integrate with it, there are no "private bits" that would make this task insurmountable, there was just not much need to do so so far, and some Linux folks (as evidenced by skimming through other .NET submissions here) tend to have irrational and unsubstantiated hatred towards .NET which hinders otherwise positive community efforts.