Every time I talk to someone about battery life on Linux vs. Windows it turns out they aren't even comparing similar hardware. Or if they are, they're comparing completely dissimilar workloads (e.g. compiling a ton of stuff while it is running Linux, basically using Chrome to look at the internet in Windows). Please note I am not saying you are incorrect. I am simply pointing out that statements like that without quantifiable data do nothing other than spread misconception.
Mind, it's not all the kernel's fault. libva/vdpau support for GPUs aren't shipped with Fedora proper, and when it's installed, GStreamer/ clutter-gst bugs keep breaking support in Videos, when it's not simply unsupported (in Wayland).
The latter parts are all being worked on, but as long as it's an optional third-party download, we won't be seeing the improvements any time soon.
Well the reason it's not included is due to legal/patent issues so it's no different than all the other codec patent issues we already have in that regard.