IPCC conclusions are unequivocal: we must divide our greenhouse gas emissions by two before 2030 if we want to maintain the global warming below 1.5°C in 2100. Hence, it becomes urgent to aim sobriety. Contrary to what is often claimed, digital technologies must also target global emission reduction, as their impact on the climate is huge and exploding every year. Among the digital world's emissions, those related to video processing and streaming are significant. At the same time, a lot of research efforts are currently done to reduce the energy consumed by video transmission algorithms or infrastructures. In this paper, we demonstrate that, even though such research works are crucial, they are not sufficient to enable global video streaming emissions reductions. The conclusion is that we must collectively think of other complementary solutions.