I have to disagree with your judgment, Dave. Rhyme can be a wonderful thing in the right setting, and sometimes outright necessary, but in the case of Wild Mountain Thyme I don't see it as necessary, or even desirable.
Wild Mountain Thyme is fairly slow, and contemplative. That verse you quoted is one single sentence, almost a spoken sentence which happens to have some tune to it. Rhyme would seem out of place,to me.