The last time I looked at ROCm (which was something like a year ago) it was "supported" as in "there's reports on the internet that someone got it to work" but when I tried, I couldn't get it to work and it really wasn't worth the effort. If I'd dig out a machine with an AMD GPU right now, can I get it working (like, train MNIST or some other helloworld'y system) within an hour, and is there documentation available on how exactly that should be done?
I think there have been a few projects that try to translate CUDA stuff into OpenCL or other AMD-compatible compute platforms.
If you're asking why AMD doesn't make a compiler for CUDA source code that targets their own GPUs--that's basically what ROCm currently does. They're pushing their CUDA alternative, called "HIP", which is essentially just CUDA code with a find-and-replace of "cuda" with "hip". (And other similarly minor changes.) They have an open source "hipify" program that does this automatically (https://github.com/ROCm-Developer-Tools/HIP/tree/master/hipi...).
So, basically, AMD GPUs are already sort of CUDA compatible: just run your CUDA code through hipify, then compile it using the HIP compiler, and run it on a ROCm-supported system (which, for now is the most spotty of all of these steps IMO).