The Cat and the Fiddle

[Hookbill the Goomba]

Good gracious me!
Well that is a question I have meant to ask myself, but never got around to it.
I think he did this to emphasise how Middle earth and all its history was written as a mythology FOR England and so had to have at least some connections with this world and time, so that people would realise this.
On another note, do you think Tolkien was putting in some tiny mention or hint of Tom Bombadill in this song?

The cat on his fiddle played hey-diddle-diddle,
A jig that would wake the dead:

A slight mention of how Tom has power over the Barrow wights?
Or is it just coincidence?
Any thoughts?