IMHO the main reason no one really bothers into dealing with directX is based on the fact that there already is a graphics library (mesa in the special case of Linux) available that fully supports any desired graphics operation also available with DirectX.
In contrast to following DirectX, which is a specification based on so called intellectual property owned by a single corparation the API used by this library called openGL is an open standard agreed upon by a consortium of hardware manufacturers.
Different from the philosophy of constraining it's use to just one operating system possibly trying to shackle its users to the one and only platform openGL was intended as a platform independent API right from the beginning.
Following this principle in contrast to DirectX being available just on one single platform openGL is available on any computing platform ranging from android based systems, Mac and numerous other UNIXoid systems including Linux even to Windows machines.
Using any other API than openGL would break this platform independence, which probably wouldn't be received as a progress but rather as a regression.
To sum it up possibly the main reasons to favor openGL over DirectX are the following:
openGL is an open standard while DirectX is proprietary
openGL is available on any platform DirectX is only available on a single platform
any operation supported by DirectX is supported by openGL as well
if they are really needed DirectX calls can be provided by a wrapper library pushing operations down to openGL as for example done in WINE
Mere availablity of a DirectX library implementation alone wouldn't enable any binary code designed for the Windows platform to run at all as the whole set of system libraries and infrastructure still would not be available at all. As a matter of fact even the binary format in use PE/COFF on Windows ELF on Linux is different.
An effort to supply a whole compatibility layer including needed system libraries is already on the way. As already mentioned above it goes by the name of WINE. (see: http://www.winehq.org/)
I hope I gave you some good reasons why no one ever tried (or will try) as you requested.