This was the case of the ruler of Ethiopia. When Muslims sought refuge there and they recited a portion of the Quran, they saw his eyes fill with tears. This is how we should be. When we hear the Quran, we should reflect on the meanings. The Quran should not become for us a replacement for pop songs that we used to hear before.
People buy recordings of their favourite reciters for the beauty of their voice.
The listening of the Quran has become more of a musical thing. We should be reading it regularly, not just during Ramadhan. We reflect on it. It really does not matter if we don't finish the Quran in Ramadhan. For most of the Prophet's Sallallahu 'Alayhi wa sallam life, he did not finish the whole Quran in Ramadhan.