By overkill I mean it might not provide additional benefit, in terms of quiet operation or CPU performance, compared to something less imposing. Something like a Dark Rock 3 for instance... or maybe even the Shadow Rock 3 I'm looking at. But then, it won't hurt performance either to be sure. But what's 'imposing' in size is where cooler choice can be a personal thing; it's my sense of aesthetic which you may or may not share.
Streaming can be a CPU burden, but I'm not sure it's all that heavy, or makes extensive use of AVX instructions. I suppose it can depending on the type of streaming and codec's though.
About that case: based on the picture of it I see I feel it could be restrictive. The front panel is mostly blocked with one opening for the one front mounted fan. That fan's in the bottom, no less, so it will be providing cool air only to the GPU...which in turn will push it's hot air up to the CPU cooler. That's not a good scenario for proper ventilation. I'd prefer a case with a full-open front with room for two or three fans behind mesh panel to allow good air flow.
There's space for three fans on the top, one in rear and two more in front though...I'm just not sure how to get enough cool air into the front through that one opening to feed both CPU and GPU without running all those case fans at high speeds...meaning noisy.
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