Heck, I don't propose trying to eliminate any old songs, especially a bangup rabble-rouser about impure blood watering our furrows. Banning music is European stuff, and just look at how well it works.
But introducing additional anthems, whether old tunes or new, old words or (usually) better ones, would mean competition. Let the band strike up something Sousa or Brahms or Scott Joplin, and we'll see how fast the crowd starts skipping and swaying and singing along.
When the time comes to roar defiance, we'll revert to la Marseillaise and Whose Side Are You On.
After all, What Shall We Do With the Drunken Sailor is set to the tune of an Irish rebellion song.