CUDA is a proprietary Nvidia product. CUDA solved the problem for Nvidia chips.
On AMD GPUs, you use ROCm. On Intel, you use OpenVINO. On Apple silicon you use MLX. All work fine with all the common AI tasks you'd want to do on self-hosted hardware. CUDA was there first and so it has a more mature ecosystem, but, so far, I've found 0 models or tasks I haven't been able to use with ROCm. llama.cpp works fine. ComfyUI works fine. Transformers library works fine. LM Studio works fine.
Unless you believe Nvidia having a monopoly on inference or training AI models is good for the world, you can't oppose all the other GPU makers having a way for their chips to be used for those purposes. CUDA is a proprietary vendor-specific solution.
Edit: But, also, Vulkan works fine on the Strix Halo. It is reliable and usually not that much slower than ROCm (and occasionally faster, somehow). Here's some benchmarks: https://kyuz0.github.io/amd-strix-halo-toolboxes/