Fine post, Mudlark. I disagree, however, with your assertions in your last couple of sentences:
'Sentimentality is all about getting the listener to respond. It's a power play'.
That may be true in some instances, but not always. Many singers sing what would be regarded by others as 'sentimental songs' because these songs have the power to move them deeply. I think particularly of Roscoe Holcomb's performance of 'Little Bessie' for Cohen. The listener had nothing to do with it, there was no thought of manipulation, but it had a profound effect on Holcomb. Cohen says that he was so emotionally drained that he refused to record for several days.