Yes, cinematographers do vary the shutter angle for artistic purposes, but that just confirms the fact that the amount of motion blur present in a film is a deliberate artistic decision rather than a side effect of using an "antiquated" frame rate.

As for downsampling, I believe your math is off. 120 fps at 360° means each frame is exposed at 1/120s. Conforming that to 24 fps gives you the same exposure duration per frame (you're just throwing out 4/5 frames), so you're effectively at a 72° shutter angle - less than half of what's considered "normal".