It's a totally reasonable question, and one that everyone asks when they're learning about CUDA. The frustrating answer to your last question is that lots of companies have shipped GPU dev environments that can theoretically be used instead of CUDA. AMD has ROCm, Apple has had a couple projects (OpenCL, Metal), Intel has some stuff, and there are newer efforts like TinyGrad + a generation of slightly higher level frameworks from AI companies, like Triton from OpenAI.
The basic problem is that CUDA has become something of a Schelling point. If you want to train a model right now, the highest performance you can get is almost certainly on CUDA. From the basic general matrix multiply operation, to specific NN architectures, CUDA is going to have incredibly optimized implementations out of the box. And it's going to make multi-GPU training so much easier. And all the dependencies you build on (those layers you import from PyTorch or Transformers or whatever) are going to work optimally right away on CUDA. And that weird random repo that you found with a unique optimizer--it runs on CUDA too. And now the cool new implementation that you're about to release is also going to be built for CUDA.
It's so tempting to think "Just write replacement software", but you also need to transition the entire ecosystem in large part to match CUDA's effectiveness, and you need to get comparable performance out of your chip/library combo as NVIDIA can get out of its cards with CUDA.
There's a whole story here to how effective NVIDIA has been at navigating this. Very early on, they heavily prioritized PyTorch and TensorFlow, getting involved in the projects as much as they could and making sure they always ran best on CUDA. But the TLDR is that yes, you're right, another company could write a CUDA competitor. But actually replacing CUDA is a much larger task.
I'm personally hopeful that with the rise of coding agents, we see more movement on this front with other projects moving into view. It will take some time for any ecosystem to start to emerge that can dislodge CUDA for researchers who don't want to dive that deep into the stack, but hopefully we start to see some momentum build.