One thing shared between old software rendered desktops and modern videogames is that they shunned these intermediate 'composited' screens. On the desktop, there used to be the screen, and basically windows used to draw on top of each other, there was no intermediate buffer for the whole window to draw itself to, which would then be smushed together with all others.
Video games are the same (mostly) - everything is rendered in screen space for performance reasons, it's very, very rare, that you would render something into a temporary buffer then composite it on top of the rest of the scene - you would need exceptional reasons for that.
Maybe it's time to get back to the olden days of display servers - where applications would push a list of render commands to the 'display server', which would consist of rendering primitives, which would then take these commands and construct the whole UI on the screen, without the intermediate steps of each app drawing into its own little buffer.
You could always fall back to drawing your own applciations, then asking the display server to composite that, but that would pretty much be the exception, not the norm.
Most games haven't rendered directly into the "screen buffer" for 15-20 years.
Vast majority of titles use deferred rendering, and lighting is done off screen too. Usually the only thing done to the "screen buffer" is a final post-process pass or a copy.
This would really help responsiveness. Keypress to pixel is a huge issue in these bloated frameworks which are running on top of bloated OS
There’s a reason why all modern desktop environments are designed the same way: power efficiency when multitasking.
Imagine you have 3 windows visible at the same time: a videogame rendering at the refresh rate of the display 144 Hz, a video player rendering frames at 30 Hz, and a text editor rendering blinking cursor at 2 Hz. Because the videogame wants to deliver frames at 144 Hz, the desktop compositor has to deliver the entire desktop at 144 Hz. Asking the video player and especially the text editor to also deliver frames at that frequency would be wasteful. Irrelevant for desktops with fast discrete GPUs, but directly translates to battery drain on laptops.