Yeah, but Auld Lang Syne ain't even about New Year's... New Year's songs are more about feel than any explicit tie to the holiday... Celebration for celebration's sake because, let's face it, as holiday's go, the New Year's holiday is based on even less tangible stuff (really, it's the celebration of having to buy a new calendar) than any of the others - even the ones that are based on complete fiction.
That said, that REM song is a perfect example of celebration for celebration's sake (with a touch of the dark side thrown in there, because, you know, one day/calendar purchase closer to the grave and all that), and while I'd rather shove a pistol down my gullet than purposely listen to that Wang Chung song ever again, that hits the spot for NYEs' songs.
My personal fave NYE song is the Grateful Dead's Sugar Magnolia, simply because for so many years it was the traditional GD NYE song. And, really, it has about as much to do as the meaningless change of numbers on a clock or a calendar as Auld Lang Syne does...
https://www.youtube.com/watch?v=2kQ1D7EpTjI