I prefer intrinsics as they give more control than shader languages and they can be written in C++ instead of fiddling with some garbage GPU API that runs async.
Also one of the reasons CUDA won developer love is that it fully embraced polyglot programming on the GPU.
CUDA seems nice, but being Nvidia only makes it a total dead end.
In what concerns commercial uses of CUDA, Hollywood doesn't seem to have any problem with it, nor the car manufacturers with Jetson.
It does look like Intel is supporting at least, so maybe in the future it will be a good option.
Or are you speaking about the 1% Linux users on Steam?
There's also HIP[1], which can be used as a thin wrapper around CUDA, or with the ROCm backend on AMD platforms. It doesn't yet match CUDA in either breadth of features or maturity, but it's getting closer every day.
I wish all the GPU companies would get together and make a standard based on C++ and stick with it.