We do hear the cumulative effect. We may not hear its small constituents in isolation though. A good way to explore the phenomenon is to take a heavily processed mix and compare it to what it used to sound before mixing and processing. The sound of the non-processed tracks is likely to have more clarity and integrity. It’s raw, it’s unfinished but somehow better-defined. Whereas the sound of the mix exhibits a generic kind of smearing that wasn’t there in the beginning. I call it ACE (the audio condom effect).