But seriously, and please note that I am not at all denying that transmission can and does happen 'orally' or 'aurally', the term 'the oral tradition' as if there were one single uninterrupted stream of heritage does annoy me because I don't think it can be right.

I think I do know roughly what you mean by it. The emphasis here is on roughly. Because even though I am sure you can provide detailed examples overall as a concept I think it might be an oversimplification.

Does 'the oral tradition' encompass Irish, Scottish and English oral/aural transmission of words and tunes, for example, or would it be better to use the plural and drop the definite article?

And it hasn't always been non-controversial and I don't think it is so now. Regarding the past, I was told to look at Wilgus and I did. I rest my case on whether the topic of oral/aural transmission and creation of material has or has not been controversial: it's the main topic of the opening of his book! Not to mention the concept of 'ballad' as equivocally used by Gummere.

Looking at it from another perspective, why not speak of transmission practices rather than use this concept which implies long lineage via oral/aural means when it seems fairly clear to me that written and oral/aural culture have been intertwined for centuries (on this I agree with Lloyd and more so, and also see the arguments of another book suggested on Mudcat, the Literary history of the ballad.