This really rings true to my early experiences with driving. As a novice, every moment driving was a sensory overload. Check the rearview mirror! Am I going at the right speed? Is anyone overtaking me? Am I staying centered in the lane? How long has that light been green? Plus all the little mechanics of actually operating a motor vehicle, actually moving your hands and feet the right amounts.
Now, a lot of getting better at driving was just building up muscle memory and good habits, yes, but I think a lot of it was really improving my selective perception and being able to quickly filter out the irrelevant to focus on exactly what was needed to drive safely and effectively.
I also play a lot of fighting games in my spare time, like Guilty Gear, and I feel this there as well. Pick up a new fighting game - especially if it's your first one - and quickly get overwhelmed by all of the things happening on the screen and all of the precise button presses you're expected to make. But then over time, you filter out all the noise and just track the minimum information - the positions of characters, the strategies, the higher-level gestalts at play - and end up spending much less cognitive effort for more effect.