Video is video and is in general more properly streamed, evicted from memory, and halted when offscreen.
"... But in the worst case all your elements might be grouped into a single layer and the browser has to repaint every single element. And, when it’s done, it still needs to upload everything to the GPU. All of this is work occurs for every GIF frame..."
GIF's are really a nineties format (90ties??), the animation and alpha components weren't added to the standard until 1989, and adoption wasn't widespread until after then.
You're also overlooking the fact that you simply didn't get 4.5MB+ GIFs in the nineties like the example given because it would take ten minutes to download that on a 56K modem. I must resign myself to the fact some people never grew up with dial-up!
Animated gifs in 1995 were rather different to animated gifs now.