I do wonder how much could be saved on energy bills for one of the most common uses of the net (watching videos), especially for folk in developing nations.

Oh dear. Video acceleration means GPU is doing what CPU would be else doing. Which means user threads get less indirect access to GPU. Which is a potential security risk, because GPUs and GL are designed to perform, not to secure data.

VA-API is not mentioned in the question at all. It is the most common api for video acceleration, but there are others - direct vdpau, or nvdec.