Pallas I'd love to hear more. Can you give an example of what you mean?
Select any song (with lyrics) that you know well, and can play from memory. Play through the song. Now add another instrument, your voice. Play and sing at the same time. How did you do?
For me, whenever I add something to a song, if the song is not completely in muscle memory, my playing will degrade. So either my singing or my playing must be in muscle memory for me to have a decent performance. Later, when both are on autopilot, I can do other things, like notice audience reaction, hear how my instrument sits in the mix, etc.
On piano, where I'm a complete novice, even the tiniest addition of workload makes it all turn to crap. That's why you can play either hand by themselves, but when you first try it hands together, it's ungood. For me at least, it would be unwise to try to play all aspects of the song at once when I start.
Later, when you are more experienced, you recognize the rhythm, chord sequences, etc. for a new song. You won't even have to think about the inversions, or how you'll musically move from chord to chord. Your fingers just know how, and do it of their own accord. That leaves you free to concentrate on other things, like "Is the drummer hitting on my girlfriend?" π
I hope that was what you had in mind with your question. Oh well. It's the Internet. You get what you get..... π