Alternatively they could make their own API, independent from OpenCL. I have written a small amount in each languages (a rainbow table generator), and found the CUDA version much more pleasant to use. CUDA made it really easy to get a good idea of the underlying hardware, and make architectural changes in order to make the code faster.

OpenCL (using an ATI card) was much harder to program, since the abstraction level was much higher. Writing two separate kernels and have them each be faster than a generic version that ends up compromising for compatibility.

The OpenCL one ended up being faster, but I suspect that's due to ATI hardware being superior at the time.

They are working on something like that - http://www.extremetech.com/extreme/218092-amds-boltzmann-ini...

The current versions only work with a couple of latest AMD chips though. And CUDA is just one part of it, they have nothing equivalent to CuDNN

1. They have no say in the API so NV would just steer the API in ways to make sure it would be suboptimal on AMD hardware.

2. It's not just the API. It's the entire SDK that has NV specific hooks that AMD can't tap into

They do. They have a retargeting compiler. It's performance sucks.