That is essentially the ultimate goal, muscle memory. Much like how people memorize insanely large combos, or on reaction reflexes from fighting games, being able to play without worrying about said song, and playing flawlessly is when you can comfortably say you have reached perfection for that piece.
However, I discovered the hard way, perfection isn't always best as I came to dislike playing my music, as it felt almost drone-like. I looked at how could I humanize my playing more - subsequently I came to an odd conclusion, stop a little bit before perfecting a song. The last video is a weird example, you can notice the mistakes, but at the same time, it's still a considerably positive performance. If I went to perfect that song, I'd possibly tarnish my thoughts of a beloved theme, and character from one of my largest influences - Touhou Project.
This play style might not suit anyone, hell it'd drive classical pianists insane, which is why I have an interest in Jazz, how loose the playing is. It's anything but drone in feeling. It's unpredictable, and can go almost anywhere with the flow. Jazz pianists do strive to perfection, but they also manage to make something beautiful, out of something messy. That's one the goals I've set for myself with the years to come.
Also thanks Frost, still not played the games, but I love the music a lot!