Many of the songs "of the people", that is to say folk songs from rural England, point morals that seem a little odd to modern urban/suburban people and as you say even a little nasty. But you have to think about where they're coming from, so to speak.None of the morals or motifs that you mention are odd in the least, but that's not the point. "The Bitter Withy" does not utilize for its instructive purposes a make-believe fairy or youthful hero/demigod who has yet to realize and tame his power, but Christ Himself. That's an important point because I think that how we speak of Christ should reflect what we believe about Who He Is, and just what that means for us and for our salvation.
Medieval folk did not put their religion into a box and just take it out on Sunday -- most went to daily Mass and religion was in everything they did.And so it should be with us. Perhaps we need to look very hard at ourselves and at our society, at why we compartmentalize things to such an extent that we separate our faith from our "secular" lives, and how the Gospel can have any meaning at all for us if our faith does not become ingrained into our very beings and manifest itself in every aspect of our lives: Every action, every thought, every breath we take should be for Christ. (Just writing this convicts me of how far I fall short. Lord have mercy, for I am a great sinner.)
All I'm saying is that if you were a 15th century yeoman or laborer somewhere out in the wilds of Wiltshire, you would probably be more focussed on the Incarnation as God made man, with emphasis on the man. Their lives were hard, often cut suddenly short, and their horizon was only as far as they could see, since they were unlettered and most never travelled more than a few miles from where they were born.
Their circumstances made their view of Christ quite different from ours, who have the luxury of literacy, easy work, and modern conveniences. It gives us a different perspective!
I think the whole point of studying history is to enable us to think ourselves into another person's head and see things from their vantage point, even if it's different from ours and in our view erroneous. C.S. Lewis recommended "reading old books" for precisely that reason, since our blind spots are not their blind spots and their mistakes are not the same as ours. It opens up your mind.