The evidence you want to see is literally something you can do or search the Internet yourself. There’s thousands of results. CPU is better than a GPU no matter codec you use. This hasn’t changed for decades. Here’s one of many direct from a software developer.
https://handbrake.fr/docs/en/latest/technical/performance.html
By being ripped out and sandboxed the same way other apps are, Google services isn’t free to siphon battery. This means you can restrict battery use and cut the constant communication down. Thus saving battery. If you allow it, yes it is not different than if it was preloaded.