The lack of CUDA support on AMD is absolutely not that AMD "couldn't" (although I certainly won't deny that their software has generally been lacking), it's clearly a strategic decision.
Supporting CUDA on AMD would only build a bigger moat for NVidia; there's no reason to cede the entire GPU programming environment to a competitor and indeed, this was a good gamble; as time goes on CUDA has become less and less essential or relevant.
Also, if you want a practical path towards drop-in replacing CUDA, you want ZLUDA; this project is interesting and kind of cool but the limitation to a C subset and no replacement libraries (BLAS, DNN, etc.) makes it not particularly useful in comparison.
Supporting CUDA on AMD would only build a bigger moat for NVidia; there's no reason to cede the entire GPU programming environment to a competitor and indeed, this was a good gamble; as time goes on CUDA has become less and less essential or relevant.
Also, if you want a practical path towards drop-in replacing CUDA, you want ZLUDA; this project is interesting and kind of cool but the limitation to a C subset and no replacement libraries (BLAS, DNN, etc.) makes it not particularly useful in comparison.