Wine exists, so we already have an open source DirectX implementation for Linux. It's not currently exactly compatible with libd3d12.so, because wine provides a Windows PE .dll, not a Unix ELF .so. Though I think Winelib may already allow you to access the Windows APIs via en ELF toolchain.

> Mesa is a freedesktop project and this is not the freedesktop I was imaginating.

Taking OpenGL and converting to a closed source device driver interface doesn't seem that different, morally, from converting to a closed source graphics driver device API.