Some of the best singers I know sing, with what can only be described, as their 'natural voice' - and, in my opinion, that is the only idiosyncracy that is required. To deliberately develop some sort of weird, strangled warble, which is then slavishly imitated by every Tom, Dick or Harry is just irritating!

Shimrod, perhaps I misunderstood your meaning. I took 'idiosyncratic' to mean having characteristics particular to an individual. Hence my comment above, that the world would be a more boring place if all singers sounded identical and didn't have individual characteristics.

But how do you know that the originator of the "weird, strangled warble" is not singing in his or her natural voice, and that they are deliberately choosing to sing like that? (But obviously, those who copy this person are not.)

Can you give any examples to illustrate what you mean? It might become clearer then.