Iona and Peter Opie (Oxford Book of Nursery Rhymes, 1951) list all the principal "allegorical" explanations, commenting:
"Other stories, giving the rhyme allegorical significance, are not so easy to disprove. Theories upon which too much ink has been expended are [list, including all those mentioned in this thread]. If any particular explanation is required of the rhyme the straightforward one that it is a description of a familiar entertainment is the most probable."
They generally knew what they were talking about.