Re: head voice: I would think it would be up to the woman herself to decide whether she wants to learn this technique. I can tell you that in my 180-voice choral group, which has performed in various venues, including the Sistine Chapel, Albert Hall, Carnegie Hall, Red Square, Sorbonne, among others, it is considered by the conductor that head voice should be part of the vocal arsenal for women. Falsetto for male voices is also fine--if the transition between full voice and falsetto is smooth--preferably so smooth as to be unnoticeable. That's the key for all voice parts--the transition must be smooth.   As you might imagine, we don't do much yodeling. Though I have nothing against yodeling. I think Elton Britt and Frank Ifield are very impressive. I just can't do it myself.

To return to the thread topic: there are quite a few songs which can be done with a limited range, including a large number of folk songs, as has been noted.. But head voice and falsetto can indeed extend the range.