I feel like I agree with you in general. However, although I didn’t make the statement previously, I think complex music does require more cognitive effort because there are more things to keep track of. It is hard to appreciate noise that seems random, so complex music requires more processing. Not defining time sigs or identifying modulations, but focusing on the details to find the patterns and make predictions.I generally don't do a lot of thinking about music when I am listening to it. I might think about some aspects of it because they interest me, but I don't think there's a requirement of thinking about music while listening to it in order to enjoy it. Music is an immersive experience for a deep listener. I don't think it involves much conscious level cognition to enjoy it, but maybe that's just the way I hear/listen, and others are different.
The point I would make in all this is that for me the idea that complex music requires a deeper cognitive effort doesn't really make sense. If I want to play it, it probably does. But as a listener, I will let it wash over me and be an experience just like any other music I might hear. I hope that makes sense.
To me recognizing a guitar from a mandolin requires thinking and you probably do that. My spouse can’t. Thinking about the chord progression would be also possible, but less likely if you are listening for pleasure. I was recently listening to a CD by Yo-Yo Ma, Edgar Meyer and Mark O’Connor and my pleasure was enhanced by trying too identify which instruments were playing the notes, which was a lot of thinking (even though I couldn’t define what was going on harmonically). I don’t normally do that, but I never play my favorite music as background music because it’s beautiful complexity just turns to noise.
But to your point, my father used to read the paper with the TV on and CDs on the carousel. If you asked him if he enjoyed the music he’d have surely said yes. I just don’t know if he’d have been able to tell you what he had just listened to. That’s the other extreme.
