Thanks for these interesting responses. I listened to a couple of Joseph Taylor and there does seem to be more of a sense of rhythm here. I note Brian's point about their being no single style.

Not being a singer, I would maybe use 'listenable' rather than 'singable', and Taylor's two pieces are quite listenable.

Pondering this, suppose you have in front of you a ballad sheet with no tune on it. It might not be written in a regular metre. I turned up one at random on the Bodleian, and in fact it isn't in a regular metre. Roud V9800 about St George and his Knights. It doesn't even have a regular number of stresses syllables per line, leave alone syllables. You try to fit it to a tune you know, and end up with something lacking rhythm, or where the emphasis of the tune falls on words that aren't naturally stressed in spoken English. You also end up having to change the tune when there are more words than your original tune has notes for.

This is without any ornamentation you decide to add to the tune, though it is of course possible to add ornamentation without losing the rhythm of the piece)

On 'melody', I am wondering whether you can have a song - as opposed to a recitation, say, without it?