(Oh, this answer is sure to confuse someone)

I feel songs should be sung asif you mean them. Sure, you can "we two, me and you" all you like, but if you're actually singing about something, it should fit you. And for some of us that'll mean they won't sing labour songs, for others that they don't sing anti-war songs (for me pro-war songs, I guess), and for some it means that the gender should match.

There's more to it than that: I don't mind as much to sing Scarborough fair, though for the second half I'm singing the wrong gender. (I guess it should be a two-gender duet). But I don't like to sing Where Do You Go To My Lovely anymore, because the person speaking is younger than me now. And there are plenty of songs I'd rather not sing because they are too feminine.

But to me the answer to the quesion is: No! I often hear good songs that I simply won't sing because they are so obviously from a female perspective. Male singers definitely do not have all the best songs.
(I did post a female version of Whisky in the Jar, once, so if you must ...)

                                                                                                                                    Mysha