"The calm within a storm". This is one of the most important aspects of the mental training benefits that sometimes goes unnoticed, from kata training. In a street self defense situation an uncluttered, calm, focused mental state, is in part what is needed to survive. I believe this is what Funakoshi meant, from your above writing.maybe that's why Funakoshi - sensei changed the name to 'heian' (Peaceful Mind)
you literally need to have a peaceful mind doing them =]