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The difference saved between an Intel & AMD system would pretty much allow a jump in tier from say a GTX 1070 to a GTX 1080Ti and net you a much bigger increase in what ever you are using it for even with the additional OBS overhead on it. Or alternatively, you could just buy a second card, GTX 1030 for £60, and then have your backup card and that would do the encoding.
I guess if you aren't looking for value per pound spent then Intel is the obvious choice, but if you even care slightly about it then Intel cannot currently be considered seriously with prices as they are.
Yes you are right in terms of money spent, and that you could buy a better card, but then you have the h.264 output quality to consider, the intel iGPU is vastly superior to nvenc for quality production. And back in the day I had an AMD card and tried doing it on that, and got missing frames and all sorts, so AMD is out the window for that kind of video processing for the way I use it.