1. No one said that you can't use CUDA for codecs, or that it won't work. It's just that h264/x264 (the codec you explicitly mentioned in your first post) WAS in NVidia's driver and they killed it because it sucked. Again, you can use CUDA for various codecs, and some map better to the GPU Architecture than others. h.264 is one that doesn't.
2. OBS uses FFMPEG and libx264 for the various codecs it supports, so the only way to get CUDA support in the various codecs is to bug the various codec library developers (the libx264 guys, the OpenJPEG guys, etc.) and the FFMPEG people to implement it. Asking here for it won't get you anywhere.
3. The issue with CUDA support is that it only works on NVidia GPUs, yet the (possibly vast) majority of GPUs used in gaming are Intel integrated GPUs, which means you're asking for a TON of work to be done by the wrong team (see point #2 above about who to bug for CUDA codec support), for a standard (CUDA) that is only supported by 1 of the 3 GPU manufacturers...
Side note: Yes, when it comes to discreet GPUs, NVidia is king, but with AMD's APUs and Intel iGPUs, Nvidia will soon be 3rd in the GPU race (and I'm saying this as someone who only owns NVidia GPUs), so putting all that work into a 3rd place company's proprietary standard isn't a good use of resources.